Bibliography. [1] Abraham, R. & J. Marsden. Foundations of Mechanics. Benjamin & Cummings, Reading, MA, 1978.


 Claribel Carroll
 1 years ago
 Views:
Transcription
1 Bibliography [1] Abraham, R. & J. Marsden. Foundations of Mechanics. Benjamin & Cummings, Reading, MA, [2] Allais, M. Economie et Interet. Imprimerie Nationale, Paris, [3] Allen, R.G.D. Mathematical Economics. (2nd edition), MacMillan, London, [4] Allen, R.G.D. Macro Economic Theory. MacMillan, London, [5] Anton, H. Elementary Linear Algebra. John Wiley & Sons, New York, [6] Anton, H. & C. Rorres. Elementary Linear Algebra with Applications. J. Wiley & Sons, New York, [7] Arnold, V. Bifurcations in Versal Families. Russian Mathematical Surveys, 27: ,1972. [8J Arnold, V.I. Mathematical Methods of Classical Mechanics. SpringerVerlag: Heidelberg, [9J Arrow, K.J. & L. Hurwicz. On the Stability of the Competitive Equilibrium, Part I  II. Econometrica 26: , October, : , January, [10] Arrow, K.J. & M. Kurz. Public Investment, The Rate of Return and Optimal Fiscal Policy. John Hopkins Press, Baltimore, Md, [11] Arrow, K.J. & M. McManus. A Note on Dynamic Stability. Econometrica: , July, [12] Arrow, K.J. & M. McManus. A Note on Dynamic Stability. Econometrica 26: , [13] Arrow, K.J., H. Block & L. Hurwicz. The Stability of Competitive Equilibrium II. Econometrica 27 (I): , January [14] Arrowsmith, D.K. & C.M. Place. An Introduction to Dynamical Stytems. Cambridge University Presss, Cambridge, [15] Athans, M. & P.L. Falb. Optimal Control. McGrawHill, New York, 1966.
2 296 [16] Bailey, N.T.J. The Mathematical Theory of Epidemics. Hafner, New York, [17] Balasko, Y. & R. Boyer. Une Analyse de l'effet du Progres Technique sur l'emploi. CEPREMAP, January [18] Barnett, S. & R.G. Cameron. Introduction to Mathematical Control Theory, 2nd edition. Clarendon, Oxford, [19] Barnett, W.A., Geweke, J. & Shell, K. Economic Complexity. Cambridge University Press, [20] Basset, L., H. Habibagachi & J. Quirk. Qualitative Economics and Morishima Matrices. Econometrica 35: , April, [21] Beckmann, M. & H. Ryder. Simultaneous Price and Quantity Adjustment in a Single Market. Econometrica 37: , July, [22] Bellman, R. Introduction to Matrix Analysis. McGrawHill, New York, [23] BenPorath, Y. The Production of Human Capital and the Life Cycle of Earnings. Journal of Political Economy 75: , [24] Benhabib, J. & R.H. Day. Rational Choice and Erratic Behaviour. Review of Economic Studies 48: ,1981. [25] Benhabib, J. & R.H. Day. Characterization of Erratic Dynamics in the Overlapping Generation Model. Journal of Economic Dynamics and Control 4: 3755, [26] Benhabib, J. & T. Miyao. Some New Results on the Dynamics of the Generalised Tobin Model. International Economic Review 22(3): , October, [27] Benhabib, J. & K. Nishimura. The Hopf Bifurcation and the Existence of Closed Orbits in Multisection Models of Optimal Economic Growth. Journal of Economic Theory 21: , December, [28] Benhabib, J. & K, Nishimura. Stability of Equilibrium in Dynamic Models of Capital Theory. International Economic Review 22: , June, [29] Benhabib, J. & K. Nishimura. Competitive Equilibrium Cycles. Journal of Economic Theory 35: , [30] Block, W.A. & J.A. Scheinkman. "Global Asymptotic Stability of Optimal Control with Applications to Dynamic Economic Theory" in Pitchford J.D. & S.J. Turnovsky (eds): Applications of Control Theory to Economic Analysis. North Holland Co., Amsterdam, [31] Boldrin, M. & L. Montrucchio. On the Indeterminary of Capital Accumulation Paths. Journal of Economic Theory 40: 2639,1986.
3 297 [32] Brock, W.A. "The Global Asymptotic Stability of Optimal Control: A Survey of Recent Results" in Intrilligator, M.D. (ed): Frontiers of Quantitative Economics. VoI3A, North Holland Co., Amsterdam, [33] Brock, W.A. & J.A. Scheinkman. Global Asymptotic Stability of Optimal Control Systems with Applications to the Theory of Economic Growth. Journal of Economic Theory 12: , February, [34] Brocker, Th. & L. Lander. Differentiable Germs and Catastrophes. Cambridge University Press, [35] Burmeister, E. & A.R. Dobell. Mathematical Theories of Economic Growth. MacMillan, London, [36] Carr, T. Applications of Centre Manifold Theory. SpringerVerlag, Heidelberg, [37] Cass, D. Optimal Growth in an Aggregate Model of Capital Accumulation: A Turnpike Theorem. Econometrica 34: October, [38] Cass, D. & K. Shell (eds). The Hamiltonian Approach to Dynamic Economics. Academic Press, New York, [39] Chang, W.W. & D.J. Smyth. The existence and Persistence of Cycles in a Nonlinear Model: Kaldor's 1940 Model Reexamined. Review of Economic Studies 38: 3744, January, [40] Chiarella, C. Elements of a Nonlinear Theory of Economic Dynamics. Lecture Notes in Economics and Mathematical Systems No SpringerVerlag, Heidelberg, [41] Chipman, J.S. The Theory of Intersectoral Money Flows and Income Formation. John Hopkins Press, Baltimore, [42] Chow, S.N. & J.K. Hale. Methods of Bifurcation Theory. SpringerVerlag, Heidelberg, [43] Clark, C. Profit Maximization and the Extinction of Animal Species. Journal of Political Economy 81: , JulyAugust, [44] Clark, Colin W. Mathematical Bioeconomics. John Wiley & Sons, New York, [45] Clark, C.W., F.H. Clarke & G.R. Munro. The Optimal Exploitation of Renewable Resource Stocks: Problems of Irreversible Investment. Econometrica 47(1): 2527, January, [46] Clarke, F.H., M.N. Darrough & J.M. Heineke. Optimal Pricing Policy in the Presence of Experience Effects. Journal of Business 55: , October, 1982.
4 298 [47] Coddington, E.A. & N. Levinson. Theory of Ordinary Differential Equations. McGrawHill, New York, [48] Colonius, F. "PoincareBendixson Theory for Control Problems with Continuous Optimal Controls", in Feichtinger, G. (ed): Optimal Control Theory and Economic Analysis 3. Elsevier Science, North Holland, [49] Conlisk, J. Quick Stability Checks and Matrix Norms. Economica (NS) XL: , November, [50] Conrad, J.M. & C.W. Clark. Natural Resource Economics. Cambridge University Press, [51] Crandall, M. & P. Rabinovitz. Bifurcation from Simple Eigenvalues. Journal of Functional Analysis 8: , [52] Cropper, M.L., D.R. Lee & S.S. Pannu. The Optimal Extinction of a Renewable Natural Resource. Journal of Environmental Economics and Management 6: , [53] Day, R.H. Irregular Growth Cycles. American Economic Review 72: , June, [54] Day, R.H. The Emergence of Chaos from Classical Economic Growth. Quarterly Journal of Economics 98: , May, [55] Day, R.H. & W.J. Shafer. Keynesian Chaos. Working Paper, Department of Economics, University of Southern California, Los Angeles, [56] DeBach, P. Biological Control of Insect Pests and Weeds. Chapman & Hall, London, [57] Debreu, G. Theory of Value. Yale University Press, New Haven, [58] Deneckere, R. & S. Pelican. Competitive Chaos. Journal of Economic Theory 40: 1325, October, [59] Denison, E.G. The Sources of Economic Growth in the U.S. and the Alternatives Before Us. Suppl. Paper No 13, C.E.D., New York, [60] Diamond, P.A. National Debt in a Neo Classical Growth Model. American Economic Review 55 (5): , December, [61] Diamond, P. Chaotic Behaviour of Systems of Difference Equations. International Journal of Systems Science 7: , [62] Dockner, E. "Local StabilityAnalysis in Optimal Control Problems with Two State Variables" in Feichtinger, G. (ed): Optimal Control and Economic Analysis 2. Elsevier Science, North Holland, Amsterdam, [63] Dockner, E.J. & G. Feichtinger. Cyclical Consumption Patterns and Rational Addiction. Vienna, undated.
5 299 [64] Dockner, E.J. & G. Feichtinger. On the Optimality of Limit Cycles in Dynamic Economic Systems. Journal of Economics 53(.): 3150, [65] Dockner, E.J., G. Feichtinger & A. Novak. Cyclical Production and Marketing Decisions: Application of Hopf Bifurcation Theory. International Journal of Systems Science, Vol 00, No 00, , [66] Domar, E.D. The Burden of Debt and the National Income. American Economic Review 34: , December, [67] Domar, E.D. Capital Expansion, Rate of Growth and Employment. Econometrica 14: , April, [68] Domar, E.D. Essays in the Theory of Growth. Oxford University Press, London, [69] Dorfman, R. An Economic Interpretation of Optimal Control Theory. American Economic Review 59: , December, [70] Dorfman, R., P.A. Samuelson & R.M. Solow. Linear Programming and Economic Analysis. McGrawHill, New York, [71] Duesenberry, J. S. Selected Problems in Economic Theory: Discussion. American Economic Review /S 49: , May, [72] Euler, L. Methodus inveniendi lineas curvas... in Opera Omnia I, V 24: , Fissli, Zurich, [73] Feichtinger, G. Limit Cycles in Dynamic Economic Systems. Annals of Operations Research. Vol 37: , August, [74] Feichtinger, G. & E.J. Dockner. Capital Accumulation, Endogenous Population Growth and Easterlin Cycles. Journal of Population Economics 3: 7387, [75] Feichtinger, G. & G. Sorger. Optimal Oscillations in Control Models: How can Constant Demand lead to Cyclical Production. Operations Research Letters 5: , [76] Feigenbaum, M.J. Quantitative Universality for a Class of Nonlinear Transformation. Journal of Statistical Physics 19: 2552, [77] Ferrar, W.L. Finite Matrices. Oxford: Clarendon Press, [78] Fiedler, M. & V. Ptak. On Matrices with Nonpositive Off Diagonal Elements and Positive Principal Minors. Czechoslov. Mathematics Journal 12: , [79J Flaschel, P. Some Stability Properties of Goodwin's Growth Cycle: A Critical Elaboration. Journal of Economics 44(1): 6369, [80] Freedman, H.I. Deterministic Mathematical Models in Population Ecology. Marcel Dekker, New York, 1980.
6 300 [81] Gabisch, G. & H.W. Lorenz. Business Cycle Theory. Lecture Notes in Economics and Mathematical Systems No 283, SpringerVerlag, [82] Gandolfo, G. Economic Dynamics: Methods of Models, second edition. North Holland, Amsterdam, [83] Gantmacher, F.R. The Theory of Matrices. Vol 1, 2, InterScience Publishers, Chelsea, New York, [84] Gardini, L., R. Lupini, C. Mammana, & M.G. Messia. Bifurcations and transitions to Chaos in the threedimensional Lotka Volterra Map. SIAM Journal Appl. Math. Vol. 47(3): , June, [85] Gause, G.F. The Struggle for Existence. Williams & Wilkins, Baltimore, [86] George, D. Equilibrium and Catastrophes in Economics. Scottish Journal of Political Economy, 28: 4362, [87] Goel, N.S., S.C. Maitra & E.W. Montroll. On the Volterra and other nonlinear models of interacting populations. Review of Modern Physics, 43: , [88] Goh, B.S. "Robust Stability Concepts of Ecosystem Models" in Halfon, E. (ed): Theoretical Systems Ecology. Academic Press, [89] Goh, B.S. Management and Analysis of Biological Populations. Elsevier Scientific Pub. G., Amsterdam, [90] Goh, B.S., G. Leitmann & T.L. Vincent. Optimal Control of a PreyPredator System. Mathematical Biosciences Vol 19: , [91] Gohberg, I., P. Lancaster & L. Rodman. Matrix Polynomials. Academic Press, New York, [92] Goodwin, R.M. Dynamic Coupling with Especial Reference to Markets Having Production Lags. Econometrica 15: , July, [93] Goodwin, R.M. The Nonlinear Accelerntor and the Persistence of Business Cycles. Econometrica 19: 117, January, [94] Goodwin, R.M. "A growth cycle" in Feinstein, C.H. (ed): Socialism, Capitalism and Economic Growth. Cambridge University Press, Cambridge, [95] Goodwin R.M. & L.F. Punzo. The Dynamics of a Capitalist Economy. Westview Press Boulder, Colorado, [96] Goodwin, R.M. et al. (eds). Nonlinear Models of Fluctuating Growth. Lecture Notes in Economics and Mathematical Systems No 228, SpringerVerlag, Heidelberg, [97] Grandmont, J.M. On Endogenous Competitive Business Cycles. Econometrica 53: , September, 1985.
7 301 [98] Grandmont, J.M. (ed). Nonlinear Economic Dynamics. Academic Press, Orlando, [99] Grimshaw, R. Nonlinear Ordinary Differential Equations. Blackwell, Oxford, [100] Guckenheimer, J. & P. Holmes. Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. 1983, 2nd edition 1986, SpringerVerlag, Heidelberg, [101] Haberler, G. Prosperity and Depression. Harvard University Press, Cambridge, Mass., 4th edition, [102] Hadley, G. Linear Algebra. AddisonWesley, Reading, MA, [103] Hahn, F. Gross Substitutes and the Dynamic Stability of General Equilibrium. Econometrica 26: , January, [104] Hahn, F. "Stability" in Arrow, K.J. & M.D. Intrilligator (eds): Handbook of Mathematical Economics. Vol II, North Holland Publishing Co, Amsterdam, [105] Hahn, F.H. On the Stability of a Pure Exchange Equilibrium. International Economic Review 3: , May, [106] Hahn, F.H. & R.C.O. Matthews. The Theory of Economic Growth: A SUnJey. Economic Journal 74: , December, [107] Halfon, E. Theoretical Systems Ecology. Academic Press, New York, [108] Harrod, R.F. An Essay in Dynamic Theory. Economic Journal 49: 1433, March, [109] Harrod, R.F. Towards a Dynamic Economics. MacMillan, London, [110] Hartman, P. Ordinary Differential Equations. Wiley, New York, [111] Hassard, B.D., N.D. Kazarinoff & U Y.H. Wan. Theory and Applications of Hopf Bifurcation. Cambridge University Press, [112] Hawkins, D. & H.A. Simon. Note: Some Conditions of Macroeconomic Stability. Econometrica 17: , JulyOctober, [113] Hicks, J.R. A Contribution to the Theory of the Trade Cycle. Oxford University Press, [114] Hilton, P.J. (ed). Structural Stability, The Theory of Catastrophes and Applications in the Sciences. Springer, Berlin, [115] Hirsch, M.W. & S. Smale. Differential Equations, Dynamical Systems and Linear Algebra. Academic Press, New York, 1974.
8 302 [116] Hussey, N.W. & L. Bravenboer, "Control of Pests in GlassHouse Culture by the Introduction of Natural Enemies" in Huffaker (ed): Biological Control. Plenum Grass, New York, [117] Inman, D.J. Vibration with Control, Measurement and Stability. Prentice Hall, New Jersey, [118] Ichimura, S. Towards a General Nonlinear Macro Dynamic Theory of Economic Fluctuations. In Kurihara, K.K. (ed.): Post Keynesian Economics: , Rutgers Univ. Press, New Brunswick, [119] Isnard, C.A. & E.C. Zeeman. Some Models from Catastrophe Theory in the Social Sciences. In Zeeman, E.C.: Catastrophe Theory: Selected Papers , AddisonWesley, Reading, MA, [120] Johnston, J. Econometric Methods. McGrawHill, New York, [121] Jorgenson. On a Dual Stability Theorem. Econometrica 28: , October, [122] Jorgenson, D.W. On stability in the sense of Harrod. Economica NS 27: , August, [123] Jorgenson, D.W. The Structure of Multisector Dynamic Models. International Economic Review 2(3): , September, [124] Kaldor, N. A Model of the Trade Cycle. Economic Journal 50: 7892, March, [125] Kaplan, W. Ordinary differential Equations. Addison Wesley, Reading, Mass, [126] Kauffman. Antichaos and Adaptation. Scientific American: 7884, August, [127] Kauffman, S.A~ Origins of Order: Self Organization and Selection in Evolution. Oxford University Press, Oxford, [128] Kelly, A. The Stable, CentreStable, Centre, CentreUnstable and Unstable Manifolds. Journal of Differential Equations 3: , [129] Kolmogorov, A. Sulla Teoria di Volterra della lotta per l'esistenzia. Gi. Inst. Ital. Attuari 7: 7480, [130] Kolmogorov, A.N. & S.V. Fomin. Elements of the Theory of Functions and Functional Analysis. Graylock Press, New York, [131] Kurz, M. The General Instability of a Class of Competitive Growth Processes. Review of Economic Studies XXXV(2): , [132] Lancaster, P. Lambda Matrices and Vibrating Systems. Pergamon Press, Elmsford, New York, 1966.
9 303 [133] Lancaster, P. Theory of Matrices. Academic Press, New York, [134] Lancaster, P. Quadratic Eigenvalue Problems. Linear Algebra and its Applications 150: , [135] Leijonhufvud, A. Effective Demand Failures. Swedish Journal of Economics 75: 2748, March, [136] Levinson, N. & O.K. Smith. A General Equation for Relaxation Oscillations. Duke Mathematical Journal 9: , [137] Lewin, R. Complexity: Science on the Edge of Chaos. MacMillan, [138] Li, T. & J. Yorke. Period Three Implies Chaos. American Mathematical Monthly 8: , [139] Lorenz, H.W. Goodwin's Nonlinear Accelerator and Chaotic Motion. Journal of Economics 47: , [140] Lorenz, H.W. "Optimal Economic Control and Chaotic Dynamics" in Feichtinger (ed): Optimal Control Theory and Economic Analysis 9. Elsevier Science Pub., Amsterdam, [141] Lorenz, E.N. Deterministic nonperiodic flow. Journal of Atmospheric Sciences 20: , [142] Lorenz, H.W. Complexity in Deterministic, Nonlinear BusinessCycle Models: Foundations, Empirical Evidence & Predictability. In Gori, F., Geronazzo, L. & M. Galeotti (etc.) Nonlinear Dynamics in Economics and Social Sciences, Lecture Notes in Economics and Mathematical Systems, No. 399, Springer Verlag, [143] Lorenz, HansWalter. Nonlinear Dynamical Economics and Chaotic Motion, 2nd edition. SpringerVerlag, Heidelberg, [144] Lotka, A.J. Elements of Physical Biology. Williams & Wilkins, Baltimore, [145] Lu, Y.C. Singularity Theory and an Introduction to Catastrophe Theory. Springer, Berlin, [146] Lucas, R.E. On the Mechanics of Economic Development. Journal of Monetary Economics 22: 342, July, [147] Majthay, A. Foundations of Catastrophe Theory. Pitman, London, [148] Marotto, F.R. SnapBack Repellers Imply Chaos in R:'. Journal of Mathematical Analysis and Applications 63: , [149] Marsden, J.E. Qualitative Methods in Bifurcation Theory. Bulletin of the American Mathematical Society 84 No 6: , November, 1978.
10 304 [150] Marsden, J.E. & M. McCracken. The Hopf Bifurcation and its Applications. SpringerVerlag, Heidelberg, [151] Marshall, A. Principles of Economics. MacMillan, London, [152] May, R.M. Limit Cycles in PredatorPrey Communities. Science 177: , [153] May, R.M. Stability and Complexity in Model Ecosystems. Princeton University Press, [154] May, R.M. Biological Populations with Non Overlapping Generations: Stable points, Stable Cycles and Chaos. Science 186: , [155] May, R.M. Simple Mathematical Models with Very Complicated Dynamics. Nature 261: , [156] McKenzie. Stability of Equilibrium and the Value of Positive Excess Demand. Econometrica 28: , July, [157] McKenzie, L.W. The Matrix with Dominant Diagonal and Economic Theory. Proceedings of a Symposium on Mathematical Methods in the Social Sciences, Stanford University Press, Palo Alto, [158] Meade, J.E. External Economies and Diseconomies in a Competitive Situation. Economic Journal G2: 5467, March, [159] Medio, A. Oscillations in Optimal Growth Models. Journal of Economic Behavior and Organisation 8: , [160] Medio, A. Oscillations in Optimal Growth Models. Journal of Economic Dynamics and Control 11: , June, [161] Medio, A. Discrete and Continuous Models of Chaotic Dynamics. Structural Change and Economic Dynamics, Vol 2: , [162] Medio, A. Chaotic Dynamics: Theory and Applications to Economics, Cambridge University Press, Cambridge, [163] Mensch, G., Kaasch, K., Kleinknecht, A. & R. Schnopp. Innovation Trends and Switching Between Full and UnderEmployment Equilibrium International Institute of Management Discussion Papers 805, January, [164] Metzler, L.A. The Nature and Stability of Inventory Cycles. Review of Economic Studies 23: , August, [165] Metzler, L. Stability of Multiple Markets: The Hicks Conditions. Econometrica 13: , October, [166] Montrucchio, L. Optimal Decisions Over Time and Strange Attractors: An Analysis by the Bellman Principle. Mathematical Modelling 7: , 1986.
11 305 [167] Moreira, H.N. On Lienard's equation and the uniqueness of Limit Cycles in predatorprey systems. Journal of Mathematical Biology 28: , [168] Morishima, M. Prices, Interest and Profits in a dynamic Leontief System. Econometrica 26: , July, [169] Morishima, M. On the three Hicksian laws of Comparative Statics. Review of Economic Studies 27: , June, [170] Morishima, M. A Reconsideration of the WalrasCasselLeontief Model of General Equilibrium. In Arrow, K.J., S. Karlin & P. Suppes (eds.): Mathematical Methods in the Social Science, 1959 Proceedings of the First Stanford Symposium, Stanford, [171] Negishi, T. The Stability of the Competitive Equilibrium: A Survey Article. Econometrica 30: ,1962. [172] Negishi, T. "Tatonnement and Recontracting" in The New Palgrave: General Equilibrium. W.W. Norton, New York, [173] Newhouse, S., D. Ruelle & F. Takens. Occurrence of Strange Axiom Attractors near QuasiPeriodic Flows on Tm (m > 3). Communications in Mathematical Physics 64: 3540, [174] Newman, P.K. Some Notes on Stability Conditions. Review of Economic Studies 27: 19, September, [175] Nikaido, H. Convex Structure and Economic Theory, Academic Press, New York, [176] Nirenberg, L. Topics in nonlinear Functional Analysis. Courant Institute of Mathematical Sciences, New York University, [177] Nitecki, Z. Differentiable Dynamics. MIT Press, Cambridge, MA, [178] Ott, Edward. Chaos in Dynamical Systems. Cambridge University Press, Cambridge, [179] Parker, F.D. "Management of Pest Populations by Manipulating Densities of both Hosts and Parasites through Periodic Releases" in Huffaker, C.B. (ed): Biological Control. Plenum Press, New York, [180] Peixoto, M.M. Structural Stability on TwoDimensional Manifolds. Topology 1: , [181] Perko, L. Differential Equations and Dynamical Systems. SpringerVerlag, Heidelberg, [182] Perlis, S. Theory of Matrices, Vol. 1. Chelsea, New York, [183] Phillips, A.W. Stabilisation Policy in a Closed Economy. Economic Journal 64: , June, 1954.
12 306 [184] Pielou, E.C. Mathematical Ecology. WileyInterscience, New York, [185] Pitchford, J.D. "Two state variable problems" in Pitchford J.D. & S.J. Turnovsky (eds): Applications of Control Theory to Economic Analysis. North Holland Co, Amsterdam, [186] Poincare, H. Sur l'equilibre d'une masse fluide animee d'un mouvement de rotation. Acta Mathematica (16 September, 1885) 7: [187] Poincare, H. Oeuvres de Henri Poincare. Tome VIII, pp Published by the Academie des Sciences GauthierVillars, Paris, [188] Pomeau, Y. & P. Manneville. Intermittent Transition to Turbulence in Dissipative Dynamical Systems. Communication in Mathematical Physics 74: , [189] Pontryagin, L.S. Ordinary Differential Equation. Addison Wesley, Reading Mass, [190] Pontryagin, L.S., V.G. Boltyanskii, R.V. Gamkrelidze & E.R. Mishchenko. The Mathematical Theory of Optimal Processes. Interscience Publishers, New York,1962. [191] Poston, T. & LN. Stewart. Taylor Expansions and Catastrophes. Pitman, London, [192] Poston, T. & LN. Stewart. Catastrophe Theory and its Applications. Pitman, London, [193] Putzer, E.J. Avoiding the Jordan Canonical Form in the Discussion of Linear Systems with Constant Coefficients. American Mathematical Monthly, Vol. 73: 27, Januar~ [194] Puu, T6nu. Nonlinear Economic Dynamics. Lecture Notes in Economics and Mathematical Systems No 336, SpringerVerlag, Heidelberg, [195] Quirk, J. & R. Rupert. Qualitative Economics and the Stability of Equilibrium. Review of Economic Studies 32: , October, [196] Ragozin, D.L. & G. Brown. Harvest Policies and Nonmarket Valuation in a PredatorPrey System. Journal of Environmental Economics and Management 12: , June, [197] Ramsey, F.P. A Mathematical Theory of Saving. Economic Journal 38: , December, [198] Rebelo, S. Long Run Policy Analysis and Long Run Growth. Working Paper, University of Rochester, Rochester, New York, [199] Rescigno, A. The Struggle for Life I: Two Species. Bull. Math. Biophysics 29: , 1967.
13 307 [200] Rescigno, A. & I.W. Richardson. On the Competitive Exclusion Principle. Bull. Math. Biophysics 27: 8589, [201] Rescigno, A. & I.W. Richardson. The Struggle for Life I: Two Species. Bull. Math. Biophysics 29: , [202] Romer, P.M. Increasing Returns and Long Run Growth. Journal of Political Economy 94(5): , October, [203] Romer, P.M. Endogenous technical change. Journal of Political Economy 98(5)II: S71S102, October, [204] Rose, H. The Possibility of Warranted Growth. Economic Journal 69: , June, [205] Rosen, R. Dynamical System Theory in Biology. Wiley Interscience, New York, [206] Rosen, R.R. (ed). Foundations of Mathematical Biology. Vol III, Academic Press, New York, [207] Rubinow, S.I. Introduction to Mathematical Biology. WileyInterscience, New York, [208] Ruelle, D. Strange Attractors. Mathematical Intelligencer 2: , [209] Ruelle D. & F. Takens. On the Nature of Turbulence. Communications in Math. Physics 20: , Also: Notes concerning our paper "On the nature of turbulence," Commun. Math. Physics 23: , [210] Samuelson, P.A. Interaction between the Multiplier Analysis and Principle of Acceleration. Review of Economic Statistics 21: 7578, May, [211] Samuelson, P.A. The Stability of Equilibrium: Comparative Statics and dynamics. Econometric 9: , April, [212] Samuelson, P.A. Foundations of Economic Analysis. Harvard University Press, Cambridge, MA, [213] Samuelson, P.A. Foundations of Economic Analysis. Harvard University Press, [214] Samuelson, P.A. An Exact ConsumptionLoan Model on Interest with or without the Social Contrivance of Money. Journal of Political Economy 66(6): , December, [215] Samuelson, P.A. A Universal Cycle. Operations Research 3: , [216] Saunders, P.T. An Introduction to Catastrophe Theory. Cambridge University Press, Cambridge, Mass, 1980.
14 308 [217] Schinasi, G.J. Fluctuations in a Dynamic, Intermediate Run ISLM Model: Applications of the PoincareBendixson Theorem. Journal of Economic Theory 28: , [218] Schultz, T.W. Investment in Human Capital. American Economic Review 51: 117, March, [219] Seierstad A. & K. Sydsaeter. Sufficient Conditions in Optimal Control Theory. International Economics Review 18(2): , June, [220] Shell, K. Toward a Theory of Inventive Activity and Capital Accumulation. American Economic Review P /P 56(2): 6268, May, [221] Silkinov, L.P. A Contribution to the Problem of the Structure of an Extended Neighbourhood of a SaddleFocus. Math. USSR Sb., 10(1): ,1970. [222] Singer, D. Stable Orbits and Bifurcation of Maps of the Interval. SIAM Journal of Applied Mathematics 35: , [223] Smale, S. Diffeomorphisms with Many Periodic Points. In Differential and Combinatorial Topology, S.S. Cairns (ed.): 6380, Princeton University Press, Princeton, [224] Smale, S. Differentiable Dynamical Systems. Bulletin of the American Mathematical Society 73: , [225] Smith, J.M. Models in Ecology. Cambridge University Press, Cambridge, [226] Smithies, A. Economic Fluctuations and Growth. Econometrica 25: 152, January, [227] Smithin, J.N. & Tu, P.N.V. Disequilibrium Adjustment in a Classical Macroeconomic Model: A Note. Journal of Economics 47(2): , [228] Solow, R.M. A Contribution to the Theory of Economic Growth. Quarterly Journal of Economics 70: 6594, February, [229] Solow, R.M. Competitive Valuation in a Dynamic InputOutput System. Econometrica 27: 3053, January, [230] Solow, R.M. Note on Uzawa's TwoSector Model of Economic Growth. Review of Economic Studies 29: 4850, October, [231] Sonnenschein, H.F. (ed). Models of Economic Dynamics. Lecture Notes in Economics and Mathematical systems No 264, SpringerVerlag, Heidelberg, [232] Stutzer, M. Chaotic Dynamics and Bifurcation in a Macro Model. Journal of Economic Dynamics and Control 2: , [233] Strang. Linear Algebra and its Applications. Academic Press, New York, 1976.
15 309 [234] Struble, R.A. Nonlinear Differential Equations. McGraw Hill, New York, [235] Swan, T.W. Economic Growth and Capital Accumulation. Economic Record 32: , November, [236] Takeuchi, Y. & N. Adachi. "Oscillations in PreyPredator Volterra Models" in Levin, S. (ed): Lecture Notes in Biomathematics. Vol 52, SpringerVerlag, [237] Tan, N.x. & P.N.V. Tu. Some Hopf Bifurcation Theorems at Simple Eigenvalues and Economic Applications. Unpublished paper, 1992, now retitled as Some New Hopf Bifurcation Theorems at Simple Eigenvalues, to appear in the forthcoming issue of Applicable Analysis, an International Journal, Vol 53/ 34, June [238] Taylor, A.E. Introduction to Functional Analysis. John Wiley, New York, [239] Thorn, R. Stabilite Structurelle et Morphogenese. Reading, Mass: Benjamin, [240] Thompson, J.M.T. & G.W. Hunt. A General Theory of Elastic Stability. Wiley, London, [241] Thompson, J.M.T. & G.W. Hunt. A Bifurcation of Theoryfor the Instabilities of Optimization and Design. Synthese, Vol. 36: , [242] Thompson, J.M.T. & H.B. Stewart. Nonlinear Dynamics and Chaos. Wiley & Sons, New York, [243] Tobin, J. Money and Economic Growth. Econometrica 33: , October, [244] Torre, V. Existence of Limit Cycles and Control in Complete Keynesian Systems by Theory of Bifurcations. Econometrica 45: , [245] Trotman, D.J.A. & E.C. Zeeman. "The Classification of Elementary Catastrophes of Co dimension ~ 5," in Hilton, P.J. (ed): Structural Stability, the Theory of catastrophes and Applications in the Science. Springer, Berlin, [246] Tu, P.N.V. The Economics of Educational Planning. Ph.D. Dissertation, A.N.U., Canberra, [247] Tu, P.N.V. Optimal Educational Investment Program in an Economic Planning Model. Canadian Journal of Economics 2: 5264, February, [248] Tu, P.N.V. A Multisectoral Model of Educational and Economic Planning. Metroeconomica 22: ,1970. [249] Tu, P.N.V. Comparative Statics and Catastrophe Theory in Economics. Discussion Papers Series No 74, University of Calgary, July, 1982.
16 310 [250] Tu, P.N.V. Introductory Optimization Dynamics. Springer Verlag, Heidelberg, [251] Tu, P.N.V. A Dynamic Macroeconomic Model. Discussion Paper Series No 102, University of Calgary, February, [252] Tu, P.N.V. Towards an Optimal Wildlife Management. Discussion Papers Series No 111, University of Calgary, June, [253] Tu, P.N.V. Introductory Optimization Dynamics. Second revised and enlarged edition, SpringerVerlag, Heidelberg, [254] Tu, P.N.V. Double Axisymmetry and Perturbed Hamiltonian Dynamical Systems in Optimal Economic Growth Models. Discussion Paper #135, Sept. 1992, Department of Economics, University of Calgary. [255] Turnovsky, S. Macroeconomic Analysis and Stabilization Policy. Cambridge Univ. Press, Cambridge, 1977, reprinted [256] Uzawa, H. On a TwoSector Model of Economic Growth. Review of Economic Studies 28: 4047, October, [257] Uzawa, H. Optimal Technical Change in an Aggregative Model of Economic Growth. International Economic Review 6: 1831, January, [258] Uzawa, H Market Allocation and Optimal Growth. Australian Economic Papers 7: 1727, June, [259] Van der Ploeg, F. Economic Growth and Conflict over the Distribution of Income. Journal of Economic Dynamics and Control 6: , [260] Van der Ploeg, F. Classical Growth Cycles. Metroeconomica 37(2): , [261] Varian, H.R. Catastrophe Theory and the Business Cycle. Economic Inquiry 17: 1428, January, [262] Velupillai, K. Some Stability Properties of Goodwin's Growth Cycles. Journal of Economics 39: , [263] Verhulst, P.F. Notice sur la loi que la population suit dans son accroissement. Correspondance Mathematique et Physique 10: , [264] Volterra, V. Lel;ons sur la theorie mathematique de la lutte pour la vze. GauthierVillars, Paris, [265] Volterra, V. Principes de biologie mathematique. Acta Biother. 3: 136, [266] Waldrop, M.M. Complexity: the Emerging Science at the Edge of Chaos. Simon & Schuster, 1992.
17 311 [267] Waltman, P.E. The Equation of Growth. Bulletin Math. Biophys. 26: 3943, [268] Wiggins, S. Introduction to Applied Nonlinear Dynamical Systems and Chaos. SpringerVerlag, Heidelberg, [269] Wilen, J. & G. Brown, Jr. Optimal Recovery Paths for Perturbations of Trophic Level Bioeconomic Systems. Journal of Environmental Economics and Management 13(3): , September, [270] Wirl, F. Routes to Cyclical Strategies in Two Dimensional Optimal Control Models: Necessary Conditions and Existence. Technical University of Vienna, [271] Wirl, F. The Ramsey Model Revisited: The Optimality of Cyclical Consumption Paths. Technical University of Vienna, [272] Wirl, F. The Ramsey Model Revisited: The Optimality of Cyclical Consumption Paths. Institute of Energy Economics, University of Vienna, January, [273] Wolfstetters. Fiscal Policy and the Classical Growth Cycle. Journal of Economics 42(4): , [274] Zarnowitz, V. Recent Work on Business Cycles in Historical Perspective: A Review of Theories and Evidence. Journal of Economic Literature 23: , June, [275] Zeeman, E.C. "Differential Equations for the Heartbeat and Nerve Impulse" in Waddington, C.H. (ed): Towards a Theoretical Biology. AldineAtherton, Chicago, [276] Zeeman, E.C. "Differential Equations for the Hearth and Nerve Impulse," in Peixoto (ed): Dynamical Systems. Academic Press, New York, [277] Zeeman, E.C. Catastrophe Theory. Scientific American 234 (PL 4): [278] Zeeman, E.C. Catastrophe Theory. Reading, Mass, Addison Wesley, 1977.
18 INDEX alimit set 150 Diffeomorphism 3 Attracting set 13 Difference Equations Attractors 13 Differential Equations 538 Asymptotic stability 100 Differential Operator D 19 Diagonalization 76 BendixsonPoincare 151 Discrete Systems 115 Bernouilli equation 11 Bifurcation Eigenspace of flow Eigenvalues 69  of map complex 69  Flip real 69  Fold 209 Eigenvectors 69  Hopf Elementary Catastrophes Pitchford 198 Equations  saddle node Bernouilli 11  supercritical characteristic 70  sub critical difference 39  transcritical differential 5 Biological control Lienard 155 Biology logistic 212 Blue Sky catastrophe Van de Pol 154 Equilibrium point 8  Exchange of Stability 195, Feigenbaum number 214 Catastrophe Theory fold Floquet Theory cusp 233 Centre Manifold Theorem Chaos First return map in map Flow 2  in flow 216 Focus 102 Characteristic exponent 185, 186 Fundamental Matrix 98 Characteristic equation 70 Characteristic polynomial 70 Gradient systems 163 Codimension 229 Growth models Competing species 288 in Economics 178,258 Complex eigenvalues 93, 120 Conservative Hamiltonian Systems 171 Cusp 233 Cycle 149 Hamiltonian flow 171 Hamiltonian function 170 Hamiltonian system HartmanGrobman Theorem 135 Homeomorphism 160 Degenerate 195,266 Homoclinic bifurcation 219 Determinants Homoclinic tangle 218
19 314 Hopf bifurcation Horseshoe map Hyperbolic fixed point Implicit Function Theorem Improper Node Idempotent matrices Intermittency ISLM economic models Jordan canonical form Lagrangian Dynamic System Laplace transformation LiYork Theorem Liapunov  characteristic exponent  function  Second method  stability LiapunovSmith reduction LienardSmith reduction Lienard system Limit Cycles Linearization theorem Manifold Map Melkinov theory Maximum Principle Morse set ,218 34, , Multiplieraccelerator models 54 Potential functions Preypredator models Repeller Saddle loop connection Saddle node Schwarzian derivative Sensitive dependence on initial conditions Silnikov Theory Singularity SmaleBirkhoff Smale horseshoe Splitting Lemma Stabilization Control models Stability  asymptotic  local asymptotic  global asymptotic  structural 163, , , , , Tatonnement Model 277 Transversality Conditions 248 Unfolding 229, 241 Unimodal Map 212 Universal Constant: Feigenbaum 214 Nilpotent matrix 87, 91 Normal forms 191 Nonhyperbolic fixed points 187,195 Nonlinear Systems Optimal Control 245 Optimal Economic growth 258 Peixoto Theorem 160 PoincareBendixson Theorem 151 Poincare map 183, 184 Poincare section 183
20 Spri ngerverlag a nd the E nvi ron ment We at SpringerVerlag firmly believe that an international science publisher has a special obligation to the environment, and our corporate policies consistently reflect this conviction. We also expect our business partners  paper mills, printers, packaging manufacturers, etc.  to commit themselves to using environmentally friendly materials and production processes. The paper in this book is made from low or nochlorine pulp and is acid free, in conformance with international standards for paper permanency.
Dynamical Systems. Pierre N.V. Tu. An Introduction with Applications in Economics and Biology Second Revised and Enlarged Edition.
Pierre N.V. Tu Dynamical Systems An Introduction with Applications in Economics and Biology Second Revised and Enlarged Edition With 105 Figures SpringerVerlag Berlin Heidelberg New York London Paris
More informationStability Analysis of UzawaLucas Endogenous Growth Model
Abstract: Stability Analysis of UzawaLucas Endogenous Growth Model William A. Barnett* University of Kansas, Lawrence and Center for Financial Stability, NY City and Taniya Ghosh Indira Gandhi Institute
More informationDIFFERENTIAL EQUATIONS, DYNAMICAL SYSTEMS, AND AN INTRODUCTION TO CHAOS
DIFFERENTIAL EQUATIONS, DYNAMICAL SYSTEMS, AND AN INTRODUCTION TO CHAOS Morris W. Hirsch University of California, Berkeley Stephen Smale University of California, Berkeley Robert L. Devaney Boston University
More informationStudies in Applied Economics
SAE./No.32/April 2015 Studies in Applied Economics Bifurcation of MacroeconoMetric Models and robustness of dynamical inferences William A. Barnett and Guo Chen Johns Hopkins Institute for Applied Economics,
More informationA Note on the Ramsey Growth Model with the von Bertalanffy Population Law
Applied Mathematical Sciences, Vol 4, 2010, no 65, 32333238 A Note on the Ramsey Growth Model with the von Bertalanffy Population aw uca Guerrini Department of Mathematics for Economic and Social Sciences
More informationNonlinear Dynamics and Chaos Summer 2011
67717 Nonlinear Dynamics and Chaos Summer 2011 Instructor: Zoubir Benzaid Phone: 4247354 Office: Swart 238 Office Hours: MTWR: 8:309:00; MTWR: 12:001:00 and by appointment. Course Content: This course
More informationThe Nonlinear Real Interest Rate Growth Model : USA
Advances in Management & Applied Economics, vol. 4, no.5, 014, 536 ISSN: 1797544 (print version), 179755(online) Scienpress Ltd, 014 The Nonlinear Real Interest Rate Growth Model : USA Vesna D. Jablanovic
More informationTHE UNIVERSITY OF KANSAS WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS SINGULARITY BIFURCATIONS. Yijun He. William A.
THE UNIVERSITY OF KANSAS WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS SINGULARITY BIFURCATIONS Yijun He Department of Economics Washington State University William A. Barnett Department of
More informationDynamics of Modified LeslieGower PredatorPrey Model with Predator Harvesting
International Journal of Basic & Applied Sciences IJBASIJENS Vol:13 No:05 55 Dynamics of Modified LeslieGower PredatorPrey Model with Predator Harvesting K. Saleh Department of Mathematics, King Fahd
More informationDIFFERENTIAL GEOMETRY APPLIED TO DYNAMICAL SYSTEMS
WORLD SCIENTIFIC SERIES ON NONLINEAR SCIENCE Series Editor: Leon O. Chua Series A Vol. 66 DIFFERENTIAL GEOMETRY APPLIED TO DYNAMICAL SYSTEMS JeanMarc Ginoux Université du Sud, France World Scientific
More information8.1 Bifurcations of Equilibria
1 81 Bifurcations of Equilibria Bifurcation theory studies qualitative changes in solutions as a parameter varies In general one could study the bifurcation theory of ODEs PDEs integrodifferential equations
More informationNONLINEAR DYNAMICS PHYS 471 & PHYS 571
NONLINEAR DYNAMICS PHYS 471 & PHYS 571 Prof. R. Gilmore 12918 X2779 robert.gilmore@drexel.edu Office hours: 14:00 Quarter: Winter, 20142015 Course Schedule: Tuesday, Thursday, 11:0012:20 Room: 12919
More informationLinearized geometric dynamics of TobinBenhabibMiyao economic flow
Linearized geometric dynamics of TobinBenhabibMiyao economic flow Constantin Udrişte and Armando Ciancio Abstract The aim of this paper is to study the influence of the EuclideanLagrangian structure
More informationAnalysis of the TakensBogdanov bifurcation on m parameterized vector fields
Analysis of the TakensBogdanov bifurcation on m parameterized vector fields Francisco Armando Carrillo Navarro, Fernando Verduzco G., Joaquín Delgado F. Programa de Doctorado en Ciencias (Matemáticas),
More informationThe Foley Liquidity / ProfitRate Cycle Model Reconsidered
MPRA Munich Personal RePEc Archive The Foley Liquidity / ProfitRate Cycle Model Reconsidered Helmar Nunes Moreira and Ricardo Azevedo Araujo and Peter Flaschel Department of Mathematics, University of
More informationQualitative analysis of the TobinBenhabibMiyao dynamical system
Qualitative analysis of the TobinBenhabibMiyao dynamical system Carlo Cattani and Armando Ciancio Abstract. The aim of this paper is to study the parametric dependence of the solutions in the TobinBenhabibMiyao
More informationWHAT IS A CHAOTIC ATTRACTOR?
WHAT IS A CHAOTIC ATTRACTOR? CLARK ROBINSON Abstract. Devaney gave a mathematical definition of the term chaos, which had earlier been introduced by Yorke. We discuss issues involved in choosing the properties
More informationChapter 1 CATASTROPHE THEORY AND THE BUSINESS CYCLE
Chapter 1 CATASTROPHE THEORY AND THE BUSINESS CYCLE We use the approach of R. Thom s Catastrophe Theory to construct a generalization of Kaldor s 1940 trade cycle. The model allows for cyclic behavior
More informationIntroduction to Dynamical Systems Basic Concepts of Dynamics
Introduction to Dynamical Systems Basic Concepts of Dynamics A dynamical system: Has a notion of state, which contains all the information upon which the dynamical system acts. A simple set of deterministic
More informationLecture 2 The Centralized Economy
Lecture 2 The Centralized Economy Economics 5118 Macroeconomic Theory Kam Yu Winter 2013 Outline 1 Introduction 2 The Basic DGE Closed Economy 3 Golden Rule Solution 4 Optimal Solution The Euler Equation
More informationMANAGEMENT AND ANALYSIS OF BIOLOGICAL POPULATIONS
',' Developments in Agricultural and ManagedForest Ecology, 8 MANAGEMENT AND ANALYSIS OF BIOLOGICAL POPULATIONS by BEANSAN GOH Department ofmathematics, University of Western Australia, Nedlands, W.A.
More informationThe PasinettiSolow Growth Model With Optimal Saving Behaviour: A Local Bifurcation Analysis
The PasinettiSolow Growth Model With Optimal Saving Behaviour: A Local Bifurcation Analysis Pasquale Commendatore 1 and Cesare Palmisani 2 1 Dipartimento di Teoria Economica e Applicazioni Università
More information2DVolterraLotka Modeling For 2 Species
Majalat AlUlum AlInsaniya wat  Tatbiqiya 2DVolterraLotka Modeling For 2 Species Alhashmi Darah 1 University of Almergeb Department of Mathematics Faculty of Science Zliten Libya. Abstract The purpose
More informationA twosector Keynesian model of business cycles
Discussion Paper No.281 A twosector Keynesian model of business cycles Hiroki Murakami Faculty of Economics, Chuo University July 2017 INSIUE OF ECONOMIC RESEARCH Chuo University okyo, Japan A twosector
More informationExistence of Singularity Bifurcation in an EulerEquations Model of the United States Economy: Grandmont was Right
MPRA Munich Personal RePEc Archive Existence of Singularity Bifurcation in an EulerEquations Model of the United States Economy: Grandmont was Right William A. Barnett and Susan He University of Kansas
More informationThe Ramsey Model. (Lecture Note, Advanced Macroeconomics, Thomas Steger, SS 2013)
The Ramsey Model (Lecture Note, Advanced Macroeconomics, Thomas Steger, SS 213) 1 Introduction The Ramsey model (or neoclassical growth model) is one of the prototype models in dynamic macroeconomics.
More informationDelay KaldorKalecki Model Revisited. September 2014
Discussion Paper No.234 Delay KaldorKalecki Model Revisited Akio Matsumoto Chuo University Ferenc Szidarovszky University of Pécs September 2014 INSTITUTE OF ECONOMIC RESEARCH Chuo University Tokyo, Japan
More informationEconomic Growth: Theory and Policy (Timo Boppart s part)
Economic Growth: Theory and Policy (Timo Boppart s part) Lecturer: Timo Boppart Stockholm University, PhD Program in Economics Q4, March/April, 2015. 1 General Information This part of the course consists
More informationOscillations in Damped Driven Pendulum: A Chaotic System
International Journal of Scientific and Innovative Mathematical Research (IJSIMR) Volume 3, Issue 10, October 2015, PP 1427 ISSN 2347307X (Print) & ISSN 23473142 (Online) www.arcjournals.org Oscillations
More informationUNIVERSITY OF VIENNA
WORKING PAPERS Cycles and chaos in the onesector growth model with elastic labor supply Gerhard Sorger May 2015 Working Paper No: 1505 DEPARTMENT OF ECONOMICS UNIVERSITY OF VIENNA All our working papers
More informationASYMPTOTIC BEHAVIOUR AND HOPF BIFURCATION OF A THREEDIMENSIONAL NONLINEAR AUTONOMOUS SYSTEM
Georgian Mathematical Journal Volume 9 (), Number, 7 6 ASYMPTOTIC BEHAVIOUR AND HOPF BIFURCATION OF A THREEDIMENSIONAL NONLINEAR AUTONOMOUS SYSTEM LENKA BARÁKOVÁ Abstract. A threedimensional real nonlinear
More informationLocal Stability Analysis of a Mathematical Model of the Interaction of Two Populations of Differential Equations (HostParasitoid)
Biology Medicine & Natural Product Chemistry ISSN: 0896514 Volume 5 Number 1 016 Pages: 914 DOI: 10.1441/biomedich.016.51.914 Local Stability Analysis of a Mathematical Model of the Interaction of Two
More information1 The Basic RBC Model
IHS 2016, Macroeconomics III Michael Reiter Ch. 1: Notes on RBC Model 1 1 The Basic RBC Model 1.1 Description of Model Variables y z k L c I w r output level of technology (exogenous) capital at end of
More informationNonlinear dynamics in the Cournot duopoly game with heterogeneous players
arxiv:nlin/0210035v1 [nlin.cd] 16 Oct 2002 Nonlinear dynamics in the Cournot duopoly game with heterogeneous players H. N. Agiza and A. A. Elsadany Department of Mathematics, Faculty of Science Mansoura
More informationThe New Palgrave: Separability
The New Palgrave: Separability Charles Blackorby Daniel Primont R. Robert Russell 1. Introduction July 29, 2006 Separability, as discussed here, refers to certain restrictions on functional representations
More informationQUADERNI DEL DIPARTIMENTO DI ECONOMIA POLITICA E STATISTICA
QUADERNI DEL DIPARTIMENTO DI ECONOMIA POLITICA E STATISTICA Ahmad K. Naimzada Serena Sordi On controlling chaos in a discrete tâtonnement process n. 729 Febbraio 216 On controlling chaos in a discrete
More informationDepartment of Economics, UCSB UC Santa Barbara
Department of Economics, UCSB UC Santa Barbara Title: Past trend versus future expectation: test of exchange rate volatility Author: Sengupta, Jati K., University of California, Santa Barbara Sfeir, Raymond,
More informationDiscrete Time or Continuous Time, That is the Question: the Case of Samuelson s MultiplierAccelerator Model
MPRA Munich Personal RePEc Archive Discrete Time or Continuous Time, That is the Question: the Case of Samuelson s MultiplierAccelerator Model Yinghao Luo 4 January 1998 Online at https://mpra.ub.unimuenchen.de/74738/
More informationComplex Systems Workshop Lecture III: Behavioral Asset Pricing Model with Heterogeneous Beliefs
Complex Systems Workshop Lecture III: Behavioral Asset Pricing Model with Heterogeneous Beliefs Cars Hommes CeNDEF, UvA CEF 2013, July 9, Vancouver Cars Hommes (CeNDEF, UvA) Complex Systems CEF 2013, Vancouver
More informationI/O monotone dynamical systems. Germán A. Enciso University of California, Irvine Eduardo Sontag, Rutgers University May 25 rd, 2011
I/O monotone dynamical systems Germán A. Enciso University of California, Irvine Eduardo Sontag, Rutgers University May 25 rd, 2011 BEFORE: Santa Barbara, January 2003 Having handed to me a photocopied
More informationUniversity population dynamics as a recontracting allocative proccess
Universidad Michoacana de San Nicolas de Hidalgo From the SelectedWorks of Teresa M. G. Da Cunha Lopes Fall September 17, 2013 University population dynamics as a recontracting allocative proccess Teresa
More informationSome Dynamical Behaviors In Lorenz Model
International Journal Of Computational Engineering Research (ijceronline.com) Vol. Issue. 7 Some Dynamical Behaviors In Lorenz Model Dr. Nabajyoti Das Assistant Professor, Department of Mathematics, Jawaharlal
More informationChaos and adaptive control in two prey, one predator system with nonlinear feedback
Chaos and adaptive control in two prey, one predator system with nonlinear feedback Awad ElGohary, a, and A.S. AlRuzaiza a a Department of Statistics and O.R., College of Science, King Saud University,
More informationLecture 4 The Centralized Economy: Extensions
Lecture 4 The Centralized Economy: Extensions Leopold von Thadden University of Mainz and ECB (on leave) Advanced Macroeconomics, Winter Term 2013 1 / 36 I Motivation This Lecture considers some applications
More informationAPPLIED NONLINEAR DYNAMICS
APPLIED NONLINEAR DYNAMICS Analytical, Computational, and Experimental Methods Ali H. Nayfeh Virginia Polytechnic Institute and State University Balakumar Balachandran University of Maryland WILEY VCH
More informationAMASES Lista delle riviste ritenute di interesse per la ricerca nell'ambito della Matematica Applicata alle Scienze Economiche e Sociali
AMASES Lista delle riviste ritenute di interesse per la ricerca nell'ambito della Matematica Applicata alle Scienze Economiche e Sociali 24 Gennaio 2010 ISI SCIMAGOJR Mathscinet Zentralblatt Econlit 4OR
More informationDynamical Systems in Biology
Dynamical Systems in Biology Hal Smith A R I Z O N A S T A T E U N I V E R S I T Y H.L. Smith (ASU) Dynamical Systems in Biology ASU, July 5, 2012 1 / 31 Outline 1 What s special about dynamical systems
More informationSufficiency Conditions for Finite Escape Times in Systems of Quadratic Differential Equations
/. Inst. Maths Applies (1977) 19, 377383 Sufficiency Conditions for Finite Escape Times in Systems of Quadratic Differential Equations W. M. GETZ AND D. H. JACOBSON National Research Institute for Mathematical
More informationAPPPHYS217 Tuesday 25 May 2010
APPPHYS7 Tuesday 5 May Our aim today is to take a brief tour of some topics in nonlinear dynamics. Some good references include: [Perko] Lawrence Perko Differential Equations and Dynamical Systems (SpringerVerlag
More informationTitle: The existence of equilibrium when excess demand obeys the weak axiom
Title: The existence of equilibrium when excess demand obeys the weak axiom Abstract: This paper gives a nonfixed point theoretic proof of equilibrium existence when the excess demand function of an exchange
More informationNonlinear MultiplierAccelerator Model with Investment and Consumption Delays
Discussion Paper No.7 Nonlinear MultiplierAccelerator Model with Investment Consumption Delays Akio Matsumoto Chuo University Ferenc Szidarovszky University of Pécs June 014 INSTITUTE OF ECONOMIC RESEARCH
More informationPart A: Answer question A1 (required), plus either question A2 or A3.
Ph.D. Core Exam  Macroeconomics 5 January 2015  8:00 am to 3:00 pm Part A: Answer question A1 (required), plus either question A2 or A3. A1 (required): Ending Quantitative Easing Now that the U.S.
More informationHOMOCLINIC CHAOS IN GENERALIZED HENONHEILES SYSTEM
Vol. 88 (1995) ACTA PHYSICA POLONICA A No. 6 HOMOCLINIC CHAOS IN GENERALIZED HENONHEILES SYSTEM S. KASPERCZUK Institute of Physics, Pedagogical University Pl. Słowiański 6, 65069 Zielona Góra, Poland
More information11. S. Jang, Dynamics of a discrete hostparasitoid system with stocking, Discrete Dynamics
Sophia Jang Department of Mathematics and Statistics Texas Tech University Office: MA202 Phone: (806) 8347006 Fax: (806) 7421112 Email: sophia.jang@ttu.edu Publications 1. M. De Silva, S. Jang, Perioddoubling
More informationTopic 6: Projected Dynamical Systems
Topic 6: Projected Dynamical Systems John F. Smith Memorial Professor and Director Virtual Center for Supernetworks Isenberg School of Management University of Massachusetts Amherst, Massachusetts 01003
More informationHelsinki: August 2006
Helsinki: August 2006 International Congress of Historical Sciences, Sydney, July 2005 International History Associatio Settler Economies in World History Part A, General Conceptual Themes usan B. Carter
More informationModeling of Chaotic Behavior in the Economic Model
Chaotic Modeling and Simulation (CMSIM) 3: 998, 06 Modeling of Chaotic Behavior in the Economic Model Volodymyr Rusyn, Oleksandr Savko Department of Radiotechnics and Information Security, Yuriy Fedkovych
More informationKeynesian Macroeconomic Theory
2 Keynesian Macroeconomic Theory 2.1. The Keynesian Consumption Function 2.2. The Complete Keynesian Model 2.3. The KeynesianCross Model 2.4. The ISLM Model 2.5. The Keynesian ADAS Model 2.6. Conclusion
More informationAn Undergraduate s Guide to the HartmanGrobman and PoincaréBendixon Theorems
An Undergraduate s Guide to the HartmanGrobman and PoincaréBendixon Theorems Scott Zimmerman MATH181HM: Dynamical Systems Spring 2008 1 Introduction The HartmanGrobman and PoincaréBendixon Theorems
More informationInputOutput Analysis Foundations and Extensions
InputOutput Analysis Foundations and Extensions Second Edition Ronald E. Miller and Peter D. Blair Hi X$P CAMBRIDGE UNIVERSITY PRESS List of Figures List of Tables Preface page xxii xxiv xxix 1 Introduction
More informationSCIENCE CITATION INDEX  MATHEMATICS, APPLIED  JOURNAL LIST Total journals: 79
SCIENCE CITATION INDEX  MATHEMATICS, APPLIED  JOURNAL LIST Total journals: 79 1. ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE ISSN: 00983500 ASSOC COMPUTING MACHINERY, 2 PENN PLAZA, STE 701, NEW YORK,
More informationChapter 4. Transition towards chaos. 4.1 Onedimensional maps
Chapter 4 Transition towards chaos In this chapter we will study how successive bifurcations can lead to chaos when a parameter is tuned. It is not an extensive review : there exists a lot of different
More informationECON0702: Mathematical Methods in Economics
ECON0702: Mathematical Methods in Economics Yulei Luo SEF of HKU January 12, 2009 Luo, Y. (SEF of HKU) MME January 12, 2009 1 / 35 Course Outline Economics: The study of the choices people (consumers,
More informationIrrational behavior in the Brown von Neumann Nash dynamics
Irrational behavior in the Brown von Neumann Nash dynamics Ulrich Berger a and Josef Hofbauer b a Vienna University of Economics and Business Administration, Department VW 5, Augasse 26, A1090 Wien,
More informationCHAOS THEORY AND EXCHANGE RATE PROBLEM
CHAOS THEORY AND EXCHANGE RATE PROBLEM Yrd. Doç. Dr TURHAN KARAGULER Beykent Universitesi, Yönetim Bilişim Sistemleri Bölümü 34900 Büyükçekmece Istanbul Tel.: (212) 872 6437 Fax: (212)8722489 email:
More informationIn these chapter 2A notes write vectors in boldface to reduce the ambiguity of the notation.
1 2 Linear Systems In these chapter 2A notes write vectors in boldface to reduce the ambiguity of the notation 21 Matrix ODEs Let and is a scalar A linear function satisfies Linear superposition ) Linear
More informationBifurcation theory of flexible exchange rates in the new Keynesian model: An Application
CMMA 1, No. 1, 113 (2016) 1 Communication in Mathematical Modeling and Applications http://ntmsci.com/cmma Bifurcation theory of flexible exchange rates in the new Keynesian model: An Application Mustafa
More informationECON 797K: Modeling growth and distribution, spring 2012 Wed 6:159pm
ECON 797K: Modeling growth and distribution, spring 2012 Wed 6:159pm Peter Skott pskott@econs.umass.edu Office: Thompson 904 Office hours: TuTh 1011am This course focuses on (i) (ii) (iii) the formal
More informationCourses: Mathematics (MATH)College: Natural Sciences & Mathematics. Any TCCN equivalents are indicated in square brackets [ ].
Courses: Mathematics (MATH)College: Natural Sciences & Mathematics Any TCCN equivalents are indicated in square brackets [ ]. MATH 1300: Fundamentals of Mathematics Cr. 3. (30). A survey of precollege
More informationWhat Is The General Mathematical Definition Of Lm Curve >>>CLICK HERE<<<
What Is The General Mathematical Definition Of Lm Curve The candela, for example, has a precise mathematical definition: In general however, the output has varied by less than 0.2 percent over the past
More informationMathematical models in economy. Short descriptions
Chapter 1 Mathematical models in economy. Short descriptions 1.1 ArrowDebreu model of an economy via Walras equilibrium problem. Let us consider first the socalled ArrowDebreu model. The presentation
More informationPROFIT FUNCTIONS. 1. REPRESENTATION OF TECHNOLOGY 1.1. Technology Sets. The technology set for a given production process is defined as
PROFIT FUNCTIONS 1. REPRESENTATION OF TECHNOLOGY 1.1. Technology Sets. The technology set for a given production process is defined as T {x, y : x ɛ R n, y ɛ R m : x can produce y} where x is a vector
More informationDRIVEN and COUPLED OSCILLATORS. I Parametric forcing The pendulum in 1:2 resonance Santiago de Compostela
DRIVEN and COUPLED OSCILLATORS I Parametric forcing The pendulum in 1:2 resonance Santiago de Compostela II Coupled oscillators Resonance tongues Huygens s synchronisation III Coupled cell system with
More informationModern Urban and Regional Economics
Modern Urban and Regional Economics SECOND EDITION Philip McCann OXFORD UNIVERSITY PRESS Contents List of figures List of tables Introduction xii xiv xvii Part I Urban and Regional Economic Models and
More informationDynamic Macroeconomics (Concepts, Techniques, Applications)
Dynamic Macroeconomics (Concepts, Techniques, Applications) this version: June 2013 Thomas Steger University of Leipzig Institute for Theoretical Economics Macroeconomics email: steger@wifa.unileipzig.de
More informationWalter M. Rusin Curriculum Vitae (October 2015)
(October 2015) Address: Oklahoma State University Department of Mathematics Stillwater, OK 74078 Office phone: (405) 7445847 Mobile phone: (612) 2453813 EMail: walter.rusin@okstate.edu Citizenship:
More informationproblem. max Both k (0) and h (0) are given at time 0. (a) Write down the HamiltonJacobiBellman (HJB) Equation in the dynamic programming
1. Endogenous Growth with Human Capital Consider the following endogenous growth model with both physical capital (k (t)) and human capital (h (t)) in continuous time. The representative household solves
More informationNational Institute of Public Finance and Policy
The Second Fundamental Theorem of Positive Economics Anjan Mukherji Working Paper No: 201298 March 2012 National Institute of Public Finance and Policy The Second Fundamental Theorem of Positive Economics
More informationEconomic Growth: Lecture 13, Stochastic Growth
14.452 Economic Growth: Lecture 13, Stochastic Growth Daron Acemoglu MIT December 10, 2013. Daron Acemoglu (MIT) Economic Growth Lecture 13 December 10, 2013. 1 / 52 Stochastic Growth Models Stochastic
More informationCharacterizing sustainability: The converse of Hartwick s rule
Journal of Economic Dynamics and Control 23 (1998) 159 165 Characterizing sustainability: The converse of Hartwick s rule Cees Withagen*, Geir B. Asheim Department of Spatial Economics, Free University
More informationFoundation of (virtually) all DSGE models (e.g., RBC model) is Solow growth model
THE BASELINE RBC MODEL: THEORY AND COMPUTATION FEBRUARY, 202 STYLIZED MACRO FACTS Foundation of (virtually all DSGE models (e.g., RBC model is Solow growth model So want/need/desire businesscycle models
More informationRoutes to Complexity in a Macroeconomic Model Described by a Noninvertible Triangular Map
Cubo A Mathematical Journal Vol.05/N ō 03 OCTOBER 2003 Routes to Complexity in a Macroeconomic Model Described by a Noninvertible Triangular Map Roberto Dieci Dipartimento di Studi Economici e Quantitativi,
More informationOne dimensional Maps
Chapter 4 One dimensional Maps The ordinary differential equation studied in chapters 13 provide a close link to actual physical systems it is easy to believe these equations provide at least an approximate
More informationON THE STABILITY OF SOME SYSTEMS OF EXPONENTIAL DIFFERENCE EQUATIONS. N. Psarros, G. Papaschinopoulos, and C.J. Schinas
Opuscula Math. 38, no. 1 2018, 95 115 https://doi.org/10.7494/opmath.2018.38.1.95 Opuscula Mathematica ON THE STABILITY OF SOME SYSTEMS OF EXPONENTIAL DIFFERENCE EQUATIONS N. Psarros, G. Papaschinopoulos,
More informationEconomic Growth: Lectures 57, Neoclassical Growth
14.452 Economic Growth: Lectures 57, Neoclassical Growth Daron Acemoglu MIT November 7, 9 and 14, 2017. Daron Acemoglu (MIT) Economic Growth Lectures 57 November 7, 9 and 14, 2017. 1 / 83 Introduction
More informationAdvanced Macroeconomics
Advanced Macroeconomics Endogenous Growth Marcin Kolasa Warsaw School of Economics Marcin Kolasa (WSE) Ad. Macro  Endogenous growth 1 / 18 Introduction The Solow and Ramsey models are exogenous growth
More informationChaos in GDP. Abstract
Chaos in GDP R. Kříž Abstract This paper presents an analysis of GDP and finds chaos in GDP. I tried to find a nonlinear lowerdimensional discrete dynamic macroeconomic model that would characterize GDP.
More informationMathematics for Economics and Finance
Mathematics for Economics and Finance Michael Harrison and Patrick Waldron B 375482 Routledge Taylor & Francis Croup LONDON AND NEW YORK Contents List of figures ix List of tables xi Foreword xiii Preface
More informationPerturbation Theory of Dynamical Systems
Perturbation Theory of Dynamical Systems arxiv:math.ho/0111178 v1 15 Nov 2001 Nils Berglund Department of Mathematics ETH Zürich 8092 Zürich Switzerland Lecture Notes Summer Semester 2001 Version: November
More informationA Hicksian multiplieraccelerator model with floor determined by capital stock
Journal of Economic Behavior & Organization Vol. 56 (2005) 331 348 A Hicksian multiplieraccelerator model with floor determined by capital stock Tönu Puu a,, Laura Gardini b, Irina Sushko c a Centre for
More informationBrown s Original Fictitious Play
manuscript No. Brown s Original Fictitious Play Ulrich Berger Vienna University of Economics, Department VW5 Augasse 26, A1090 Vienna, Austria email: ulrich.berger@wuwien.ac.at March 2005 Abstract
More informationSensitivity Analysis of Stationary Title Optimal Growth : a Differentiable A. Citation Hitotsubashi journal of economics,
Sensitivity Analysis of Stationary Title Optimal Growth : a Differentiable A Author(s) Sagara, Nobusumi Citation Hitotsubashi journal of economics, Issue 200706 Date Type Departmental Bulletin Paper Text
More informationThis PDF is a selection from an outofprint volume from the National Bureau of Economic Research
This PDF is a selection from an outofprint volume from the National Bureau of Economic Research Volume Title: A Theoretical Framework for Monetary Analysis Volume Author/Editor: Milton Friedman Volume
More informationA short introduction with a view toward examples. Short presentation for the students of: Dynamical Systems and Complexity Summer School Volos, 2017
A short introduction with a view toward examples Center of Research and Applications of Nonlinear (CRANS) Department of Mathematics University of Patras Greece sanastassiou@gmail.com Short presentation
More informationLocal disaggregation of demand and excess demand functions: a new question
Local disaggregation of demand and excess demand functions: a new question PierreAndre Chiappori Ivar Ekeland y Martin Browning z January 1999 Abstract The literature on the characterization of aggregate
More informationPhysics: springmass system, planet motion, pendulum. Biology: ecology problem, neural conduction, epidemics
Applications of nonlinear ODE systems: Physics: springmass system, planet motion, pendulum Chemistry: mixing problems, chemical reactions Biology: ecology problem, neural conduction, epidemics Economy:
More informationA f = A f (x)dx, 55 M F ds = M F,T ds, 204 M F N dv n 1, 199 !, 197. M M F,N ds = M F ds, 199 (Δ,')! = '(Δ)!, 187
References 1. T.M. Apostol; Mathematical Analysis, 2nd edition, AddisonWesley Publishing Co., Reading, Mass. London Don Mills, Ont., 1974. 2. T.M. Apostol; Calculus Vol. 2: Multivariable Calculus and
More informationarxiv: v1 [math.ds] 26 Jun 2017
Optimal equilibrium for a reformulated Samuelson economical model arxiv:1706.08298v1 [math.ds] 26 Jun 2017 Fernando Ortega 1, Maria Philomena Barros 1, Grigoris Kalogeropoulos 2 1 Universitat Autonoma
More informationNonRobust Dynamic Inferences from Macroeconometric Models: Bifurcation Stratification of Confidence Regions
MPRA Munich Personal RePEc Archive NonRobust Dynamic Inferences from Macroeconometric Models: Bifurcation Stratification of Confidence Regions William A. Barnett and Evgeniya Duzhak. October 006 Online
More informationAn InputOutput Pollution Control Model and Product Selection
Journal of Mathematics Research; Vol. 4, No. 5; 2012 ISSN 19169795 EISSN 19169809 Published by Canadian Center of Science and Education An InputOutput Pollution Control Model and Product Selection
More information