A New Modified Hyperchaotic Finance System and its Control
|
|
- Dennis Bennett
- 5 years ago
- Views:
Transcription
1 ISSN (print), (online) International Journal of Nonlinear Science Vol.8(2009) No.1,pp A New Modified Hyperchaotic Finance System and its Control Juan Ding, Weiguo Yang, Hongxing Yao Faculty of science, Jiangsu University, Zhenjiang, Jiangsu, , China (Received 30 July 2008, accepted 9 April 2009) Astract: In this letter, a new four-dimensional continuous autonomous hyperchaotic system, which is constructed ased on a modified finance system y introducing a nonlinear state feedack controller. The detailed dynamical ehaviors of this hyperchaotic system are further investigated, including equliria and staility, various attractors, ifurcation analysis, and Lyapunov exponents spectrum. Furthermore, effective speed feedack controllers are designed for stailizing hyperchaos to unstale equilirium points. Numerical simulations are given to illustrate and verify the results. Keywords: hyperchaos; speed feedack control; Lyapunov exponent; ifurcation MSC: O415.5;TP Introduction In recent years, chaos control and synchronization, including chaotification of dynamical system, have een received more attention due to its potential applications to physics, chemical reactor, control theory, iological networks,artificial neural networks, telecommunications and secure communication [1 6]. Many methods have een used to control dynamical system [1-6,22]. For instance, OGY method, differential geometric method, linear state space feedack, inverse optimal control and output feedack control, among many others. For feedack control, we often multiply the independent variale of system functions with coefficient and take the result as a feedack gain, so the method is called of displacement feedack control. Similarly, if we multiply the derivative of independent variale with coefficient, we call it speed feedack control[7]. If the feedack gain satisfies certain conditions, the chaotic system can e controlled to unstale equilirium points. Hyperchaotic system is usually defined as a chaotic system with more than one positive Lyapunov exponent[5,8-9]. Historically, hyperchaos was firstly reported y Rössler. That is, the noted four-dimensional hyperchaotic Rössler system [5]. Over the last two decades, some interesting hyperchaos generators were demonstrated and their dynamics have een investigated extensively in [10-14] over the past decades ecause of their useful application in engineering. As we know now, there are many hyperchaotic systems discovered in the high-dimensional social and economical systems [15-17]. A new hyperchaotic finance system is constructed in this Letter, and stailization of the hyperchaotic finance system is achieved. This letter is presented as follows: in the next section, the controlled finance system showing hyperchaotic ehavior is constructed via introducing a state feedack. In the third section, properties and dynamics of the controlled system are investigated numerically via ifurcation diagram, Lyapunov exponents. And in the last section, simple ut effective speed feedack controllers are designed for stailizing the hyperchaotic system to unstale equilirium. Furthermore, all aove dynamical ehaviors are verified y numerical simulation. Corresponding author. address: doudou@ujs.edu.cn Copyright c World Academic Press, World Academic Union IJNS.2009.xx.15/xxx
2 60 International Journal of Nonlinear Science,Vol.8(2009),No.1,pp Construction of the hyperchaotic finance system Recent works [18-20] have reported a dynamic model of finance, composed of three first-order differential equations.the model descries the time variations of three state variales: the interest rate x, the investment demand y, and the price index z, By choosing an appropriate coordinate system and setting appropriate dimensions for each state variale, references [18-20] offer the simplified finance system as ẋ = a(x + y) ẏ = y axz z = + axy where a, are system parameters.when a = 3, = 15, it shows chaotic ehavior.the strange attractor of the system is illustated in Fig.1. In light of the thought of G. Chen [17], we construct a hyperchaotic finance (1) Figure 1: Strange attractor of finance system (1). system y introducing a state feedack controller w to the system (1). The new controlled system has the form of ẋ = a(x + y) + w ẏ = y axz (2) ż = + axy ẇ = cxz dw where a, are the parameters of the system (1), and c is constant(where c=0.2), and d is the control parameter.when parameters a = 3, = 15, c = 0.2 and d= 0.12, the four Lyapunov exponents of the controlled system (2) calculated with Wolf algorithm [21] are , , 0 and Therefore, the controlled system (2) with parameter d= 0.12 shows hyperchaotic ehavior. Our numerical experiments show that system (2) has hyperchaotic attractors for a = 3, = 15, c = 0.2,d= 0.12 as depicted in Fig. 2(a) (j). 3 Dynamics analysis the hyperchaotic finance system This section further investigates the asic dynamical ehaviors of system (2). Oviously, from system (2), one has V = ẋ x + ẏ y + ż z + ẇ w Therefore, to make system (2) e dissipative, it is required that a + d + 1 > 0. = (a + d + 1) IJNS for contriution: editor@nonlinearscience.org.uk
3 J. Ding, W. Yang, H. Yao: A New Modified Hyperchaotic Finance System and its Control (a) 3D view in the x y w space () 3D view in the x z w space. (c) 3D view in the y z w space. (d) 3D view in the x y z space. (e) Projection on the x w plane. (f) Projection on the x y plane. (g) Projection on the z w plane. (h) Projection on the y z plane. (i) Projection on the x z plane. (j) Projection on the y w plane. Figure 2: Phase portraits of hyperchaotic finance system (2). IJNS homepage: 61
4 62 International Journal of Nonlinear Science,Vol.8(2009),No.1,pp The equiliria of system (2) satisfies the following equations: a(x + y) + w = 0 y axz = 0 + axy = 0 cxz dw = 0 When the parameters a,, c, d satisfy ad(a 2 d c) > 0, the system (2) has two equilirium points: P 1 ( a a 2 d c ad, ad a 2 d c, ad a 2 d c, c ad ad a 2 d c ) = ( 2,,, c ad ), P 2 ( a 2 d c ad a ad, a 2 d c, ad a 2 d c, c ad ad a 2 d c ) = ( 2,,, c ad ), ad where = a 2 d c.oviously, P 1 and P 2 are symmetric aout x, y, w-axis for any parameters a,, c, d. At the equilirium pointsp 1, the Jacoian matrix is a a J P1 = (3) c 2 c 0 d which results in the characteristic polynomial: λ 4 + (1 + a + d)λ 3 + (a + d + ad + ac2 d+ad a 3 d (a 2 d c) )λ 2 +(2a 2 c + ad ac+dc ad )λ + 2(a 2 d c) = 0. (4) Using Routh Hurwitz criterion, it is easy to show that when a = 3, = 15, c = 0.2, d = Some eigenvalues of the characteristic polynomial of the Jacoian matrix (3) has positive real parts. Thus the equilirium point P 1 is unstale. Similarly, the equilirium point P 2 is unstale. To investigate the impact of parameter d on the dynamics of the controlled system, we extend the range of d to an interval [0,0.35] and give the initial condition (0.1,-0.1,0.1,0.1), ifurcation diagram with respect to parameter d generated from the Poincaré section method is shown in Fig. 3, and the corresponding Lyapunov exponent spectrum calculated with the Wolf algorithm [21] is given in Fig. 4. Figs. 3 and 4 show how the dynamics of the controlled system(2) changes with the increasing value of the parameter d. Figure 3: Bifurcation diagram of the controlled system (2) versus parameter d, generated y the Poincaré section method. IJNS for contriution: editor@nonlinearscience.org.uk
5 J. Ding, W. Yang, H. Yao: A New Modified Hyperchaotic Finance System and its Control 63 Assume that the Lyapunov exponents of system (2) are L i for i = 1, 2, 3, 4satisfying L 1 > L 2 > L 3 > L 4. The dynamical ehaviors of system (2) can e classified as follows ased on the Lyapunov exponents: (1) For L 1 > L 2 > 0, L 3 = 0 or L 3 > 0, L 4 < 0 and L 1 + L 2 + L 4 < 0,system (2) is hyperchaos. (2) For L 1 > 0, L 2 = 0, L 4 < L 3 < 0 and L 1 + L 3 + L 4 < 0,system (2) is chaos. (3) For L 1 < 0, L 2 < 0, L 3 < 0, L 4 < 0, system (2) is an equilirium point. (a) () Figure 4: Corresponding Lyapunov exponents of the controlled system (2) versus parameter d. 4 Hyperchaos control for the hyperchaotic system For the feedack control, the independent variale of a system function is often multiplied y a coefficient as the feedack gain, so the method is called displacement feedack control. Similarly, if the derivative of an independent variale is multiplied y a coefficient as the feedack gain, it is called speed feedack control. Suppose the following autonomic chaos system: Ẋ = AX + f(x), where X = (x 1, x 2,..., x n ) T, A = (a ij ) n n, f(x) is a nonlinear function, whenx 0 0, the system is chaotic or hyperchaotic. Then speed feedack control is presented as kẋ i feedack in the right side of the equation of x j (where k > 0, i j). As a whole system, changes of a certain variale can have relative influence upon the other variales. when x i is increasing, ẋ i > 0 and the feedack gain kẋ i < 0; when x i is decreasing, ẋ i < 0and the feedack gain kẋ i > 0. As a result, the system could achieve an anti-stailization alanced degree y control when coefficient k satisfies some conditions. Let the controlled hyperchaotic system is ẋ = a(x + y) + w ẏ = y axz ż = + axy kẋ ẇ = cxz dw where k is the feedack coefficient. When k < the system (5) will gradually converge to unsteadily equilirium point P 1 ( 2,,, c ad ) andp 2( 2,,, c ad ). Proof. At the equilirium pointsp 1,the Jacoian matrix of the congtrolled system (5) is a a J = 1 0 ak + ak 0 k, c 2 c 0 d then the characteristic equation is (5) λ 4 + (a + d + 1)λ 3 + (a + d + ad + ck a2 k ( c + ck +ad2 +a 2 +a 3 2 a 2 dk c+a2 2 )λ )λ + 2(a 2 d c) = 0 (6) IJNS homepage:
6 64 International Journal of Nonlinear Science,Vol.8(2009),No.1,pp Because it is difficult to solve Esq. (6), we will give out the value data area of simulation in the following text. After complicated calculations, we get the range of the control gain, k < which can ensure that the controlled system (5) is asymptocally stale at the equilirium points P 1. To verify the validity of the staility condition otained aove, we choose the control gaink = The four characteristic values of the Jacoian matrix are , and ± i. Consequently, the controlled system is asymptotically stale at the origin. The time responses of states of the controlled system withk = are shown in Fig. 5(a). The controllers are activated at t = 10. It can e seen from the simulations that the hyperchaotic state is quickly settled down to the unstale equilirium points P 1. But the controlled system will ecome unstale if feedack coefficientk= They are shown in Fig. 5().Therefore the original proposition k < is resulted. Selecting the control gain k = , the Lyapunov exponents of the controlled system (5) are 0,0, and The time evolution of the Lyapunov exponents of the controlled system (5) with k= are shown in Fig.6. (a) Time responses of the states of the controlled system(5) with control gain.k= () Time responses of the states of the controlled system(5) with control gain k= Figure 5: The difference of the states of the controlled system (5) with the control gain change. Figure 6: Time evolution of the Lyapunov exponents of the controlled system(5) with k= Figure 7: Time evolution of the Lyapunov exponents of the controlled system (7) with k=-13. Choose the controller kẋ, and adds it to the second equation of the hyperchaotic system, we otain the following controlled hyperchaotic system: ẋ = a(x + y) + w ẏ = y axz kẋ ż = + axy ẇ = cxz dw (7) IJNS for contriution: editor@nonlinearscience.org.uk
7 J. Ding, W. Yang, H. Yao: A New Modified Hyperchaotic Finance System and its Control 65 where k is the control gain. When k < 1 the system (7) will gradually converge to unstale equilirium point P 1 and P 2 Selecting the control gain k= -13, and using the Wolf algorithm [21], we otain the following Lyapunov exponents 0, , and From these Lyapunov exponents,we can know that the controller kẋ can stailize the hyperchaotic system (7) to the unstale equilirium pointsp 1. The time evolutions of the Lyapunov exponents are shown in Fig. 7. The time responses of states of the controlled system with k = 13 are shown in Fig. 8. The equilirium point of controlled system (7) with k = 13 are shown in Fig. 9. Figure 8: Time responses of the states of the controlled (7). Figure 9: The equilirium point of controlled system (7) with k=-13 k= Conclusion In this Letter, a new hyperchaotic finance system is uilt. Some asic dynamical ehaviors are further explored y calculating its Lyapunov exponent spectrum and ifurcation diagrams. The new hyperchaotic system has more complex dynamical ehaviors than the normal chaotic systems. Effective speed feedack controllers are designed for stailizing hyperchaos to unstale equilirium. Numerical simulations are proposed to verify and illustrate the effectiveness of these controllers. It is elieved that the system will have road applications in various chaos-ased information systems. Acknowledgements This research was supported y the National Nature Science Foundation of China ( No ) and (No ). References [1] G. Chen, X. Dong: From Chaos to Order: Perspectives, Methodologies and Applications,World Scientific,Singapore.157-( 1998) [2] E.Ott, C.Greogi, J.A.Yorke: Controlling chaos. Phys. Rev. Lett. 64: (1990) [3] Dianchen Lu,Aicheng Wang, Xiandong Tian: Control and Synchronization of a New Hyperchaotic System With Unknown Parameters. International Journal of Nonlinear Science. 3(6): (2008) [4] Xuein Zhang, Honglan Zhu: Anti- synchronization of Two Different Hyperchaotic Systems via Active and Adaptive Control. International Journal of Nonlinear Science. 3(6): (2008) [5] O.E. Rössler: An equation for hyperchaos. Phys. Lett. A.71(2-3): (1979) IJNS homepage:
8 66 International Journal of Nonlinear Science,Vol.8(2009),No.1,pp [6] Ju H. Park.: Adaptive controller design for modified projective synchronization of Genesio Tesi chaotic system with uncertain parameters. Choas, Solitons and Fractals. 34: (2007) [7] H. N. Agiza: Controlling chaos for the dynamical system of coupled dynamos. Chaos, Solitons & Fractals.13: (2002) [8] A. Ĉenys, A.Tamaŝeviĉius, A. Baziliauskas: Hyperchaos in coupled Colpitts oscillators. Chaos, Solitons Fractals. 17 (2-3): (2003) [9] D.Cafagna, G.Grassi: New 3D scroll attractors on hyperchaotic Chua s circuits forming a ring. Int. J. Bifurcat. Chaos. 13 (10): (2003) [10] T. Matsumoto, L.O. Chua, K. Koayashi: Hyperchaos: laoratory experiment and numerical confirmation. IEEE. Trans. Circuits. Syst. CAS. 33: (1986) [11] Hua Chen, Mei Sun: Generalized projective synchronization of the energy resource system. International Journal of Nonlinear Science. 2(3): (2006) [12] Y.Takahashi, H.Nakano, T.Saito: A simple hyperchaos generator ased on impulsive switching. IEEE. Trans. Circuits. Syst. II. 51: (2004) [13] A.Tamasevicuius, A.Cenys: Hyperchaotic oscillator with gyrators. Electron. Lett.33: (1997) [14] T. Tsuone, T. Saito: Hyperchaos from a 4-D manifold piecewiselinear system, IEEE. Trans. Circuits. Syst. I. 45: (1998) [15] C.Z.Ning, H.Haken: Detuned lasers and the complex Lorenz equations: sucritical and super-critical Hopf ifurcations.phys. Rev. A. 41: (1990) [16] T.Kapitaniak, L.O.Chua: Hyperchaotic attractor of unidirectionally coupled Chua s circuit, Int. J. Bifurcat. Chaos. 4(2): (1994) [17] Y.X. Li, W.K.S.Tang, G.Chen: Generating Hyperchaos via State Feedack Control.Int. J. Bifurcat. Chaos.15(10): (2005) [18] J.H. Ma, Y.S.Chen: Study for the ifurcation topological structure and the gloal complicated character of a kind of nonlinear finance system (I).Appl. Math. Mech. (Englished.) 22: (2001) [19] J.H. Ma, Y.S.Chen: Study for the ifurcation topological structure and the gloal complicated character of a kind of nonlinear finance system (II). Appl. Math. Mech. (Englished.) 22: (2001) [20] J.H.Ma, R.B, Y.S Chen: Impulsive control of chaotic Attractors in Nonlinear Chaotic systems. Appl. Math. Mech. 25: (2004) [21] A.Wolf, J.B.Swift, H.L.Swinney, A.W.John: Determining Lyapunov exponents from a time series. Physica D. 16: (1985) [22] Guoliang Cai, Wentao Tu: Adaptive Backstepping Control of the Uncertain Unified Chaotic System. International Journal of Nonlinear Science. 4(1):17-24(2007) IJNS for contriution: editor@nonlinearscience.org.uk
A Novel Hyperchaotic System and Its Control
1371371371371378 Journal of Uncertain Systems Vol.3, No., pp.137-144, 009 Online at: www.jus.org.uk A Novel Hyperchaotic System and Its Control Jiang Xu, Gouliang Cai, Song Zheng School of Mathematics
More informationA New Finance Chaotic Attractor
ISSN 1749-3889(print),1749-3897(online) International Journal of Nonlinear Science Vol. 3 (2007) No. 3, pp. 213-220 A New Finance Chaotic Attractor Guoliang Cai +1,Juanjuan Huang 1,2 1 Nonlinear Scientific
More information3. Controlling the time delay hyper chaotic Lorenz system via back stepping control
ISSN 1746-7659, England, UK Journal of Information and Computing Science Vol 10, No 2, 2015, pp 148-153 Chaos control of hyper chaotic delay Lorenz system via back stepping method Hanping Chen 1 Xuerong
More informationHyperchaos and hyperchaos control of the sinusoidally forced simplified Lorenz system
Nonlinear Dyn (2012) 69:1383 1391 DOI 10.1007/s11071-012-0354-x ORIGINAL PAPER Hyperchaos and hyperchaos control of the sinusoidally forced simplified Lorenz system Keihui Sun Xuan Liu Congxu Zhu J.C.
More informationGenerating a Complex Form of Chaotic Pan System and its Behavior
Appl. Math. Inf. Sci. 9, No. 5, 2553-2557 (2015) 2553 Applied Mathematics & Information Sciences An International Journal http://dx.doi.org/10.12785/amis/090540 Generating a Complex Form of Chaotic Pan
More informationComplete Synchronization, Anti-synchronization and Hybrid Synchronization Between Two Different 4D Nonlinear Dynamical Systems
Mathematics Letters 2016; 2(5): 36-41 http://www.sciencepublishinggroup.com/j/ml doi: 10.11648/j.ml.20160205.12 Complete Synchronization, Anti-synchronization and Hybrid Synchronization Between Two Different
More informationStability and hybrid synchronization of a time-delay financial hyperchaotic system
ISSN 76-7659 England UK Journal of Information and Computing Science Vol. No. 5 pp. 89-98 Stability and hybrid synchronization of a time-delay financial hyperchaotic system Lingling Zhang Guoliang Cai
More informationGLOBAL CHAOS SYNCHRONIZATION OF HYPERCHAOTIC QI AND HYPERCHAOTIC JHA SYSTEMS BY ACTIVE NONLINEAR CONTROL
GLOBAL CHAOS SYNCHRONIZATION OF HYPERCHAOTIC QI AND HYPERCHAOTIC JHA SYSTEMS BY ACTIVE NONLINEAR CONTROL Sundarapandian Vaidyanathan 1 1 Research and Development Centre, Vel Tech Dr. RR & Dr. SR Technical
More informationGenerating hyperchaotic Lu attractor via state feedback control
Physica A 364 (06) 3 1 www.elsevier.com/locate/physa Generating hyperchaotic Lu attractor via state feedback control Aimin Chen a, Junan Lu a, Jinhu Lu b,, Simin Yu c a College of Mathematics and Statistics,
More informationThe Application of Contraction Theory in Synchronization of Coupled Chen Systems
ISSN 1749-3889 (print), 1749-3897 (online) International Journal of Nonlinear Science Vol.9(2010) No.1,pp.72-77 The Application of Contraction Theory in Synchronization of Coupled Chen Systems Hongxing
More informationStability and Projective Synchronization in Multiple Delay Rössler System
ISSN 1749-3889 (print), 1749-3897 (online) International Journal of Nonlinear Science Vol.7(29) No.2,pp.27-214 Stability and Projective Synchronization in Multiple Delay Rössler System Dibakar Ghosh Department
More informationControlling the Period-Doubling Bifurcation of Logistic Model
ISSN 1749-3889 (print), 1749-3897 (online) International Journal of Nonlinear Science Vol.20(2015) No.3,pp.174-178 Controlling the Period-Doubling Bifurcation of Logistic Model Zhiqian Wang 1, Jiashi Tang
More informationConstruction of four dimensional chaotic finance model and its applications
Volume 8 No. 8, 7-87 ISSN: 34-3395 (on-line version) url: http://acadpubl.eu/hub ijpam.eu Construction of four dimensional chaotic finance model and its applications Dharmendra Kumar and Sachin Kumar Department
More informationAnti-synchronization of a new hyperchaotic system via small-gain theorem
Anti-synchronization of a new hyperchaotic system via small-gain theorem Xiao Jian( ) College of Mathematics and Statistics, Chongqing University, Chongqing 400044, China (Received 8 February 2010; revised
More informationHYBRID CHAOS SYNCHRONIZATION OF HYPERCHAOTIC LIU AND HYPERCHAOTIC CHEN SYSTEMS BY ACTIVE NONLINEAR CONTROL
HYBRID CHAOS SYNCHRONIZATION OF HYPERCHAOTIC LIU AND HYPERCHAOTIC CHEN SYSTEMS BY ACTIVE NONLINEAR CONTROL Sundarapandian Vaidyanathan 1 1 Research and Development Centre, Vel Tech Dr. RR & Dr. SR Technical
More informationDynamical analysis and circuit simulation of a new three-dimensional chaotic system
Dynamical analysis and circuit simulation of a new three-dimensional chaotic system Wang Ai-Yuan( 王爱元 ) a)b) and Ling Zhi-Hao( 凌志浩 ) a) a) Department of Automation, East China University of Science and
More informationDynamical Behavior And Synchronization Of Chaotic Chemical Reactors Model
Iranian Journal of Mathematical Chemistry, Vol. 6, No. 1, March 2015, pp. 81 92 IJMC Dynamical Behavior And Synchronization Of Chaotic Chemical Reactors Model HOSSEIN KHEIRI 1 AND BASHIR NADERI 2 1 Faculty
More informationInverse optimal control of hyperchaotic finance system
ISSN 1 746-7233, England, UK World Journal of Modelling and Simulation Vol. 10 (2014) No. 2, pp. 83-91 Inverse optimal control of hyperchaotic finance system Changzhong Chen 1,3, Tao Fan 1,3, Bangrong
More informationSIMPLE CHAOTIC FLOWS WITH ONE STABLE EQUILIBRIUM
International Journal of Bifurcation and Chaos, Vol. 23, No. 11 (2013) 1350188 (7 pages) c World Scientific Publishing Company DOI: 10.1142/S0218127413501885 SIMPLE CHAOTIC FLOWS WITH ONE STABLE EQUILIBRIUM
More informationCONTROLLING CHAOTIC DYNAMICS USING BACKSTEPPING DESIGN WITH APPLICATION TO THE LORENZ SYSTEM AND CHUA S CIRCUIT
Letters International Journal of Bifurcation and Chaos, Vol. 9, No. 7 (1999) 1425 1434 c World Scientific Publishing Company CONTROLLING CHAOTIC DYNAMICS USING BACKSTEPPING DESIGN WITH APPLICATION TO THE
More informationHX-TYPE CHAOTIC (HYPERCHAOTIC) SYSTEM BASED ON FUZZY INFERENCE MODELING
ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS N. 39 28 (73 88) 73 HX-TYPE CHAOTIC (HYPERCHAOTIC) SYSTEM BASED ON FUZZY INFERENCE MODELING Baojie Zhang Institute of Applied Mathematics Qujing Normal University
More informationTHE ACTIVE CONTROLLER DESIGN FOR ACHIEVING GENERALIZED PROJECTIVE SYNCHRONIZATION OF HYPERCHAOTIC LÜ AND HYPERCHAOTIC CAI SYSTEMS
THE ACTIVE CONTROLLER DESIGN FOR ACHIEVING GENERALIZED PROJECTIVE SYNCHRONIZATION OF HYPERCHAOTIC LÜ AND HYPERCHAOTIC CAI SYSTEMS Sarasu Pakiriswamy 1 and Sundarapandian Vaidyanathan 1 1 Department of
More informationHopf Bifurcation and Limit Cycle Analysis of the Rikitake System
ISSN 749-3889 (print), 749-3897 (online) International Journal of Nonlinear Science Vol.4(0) No.,pp.-5 Hopf Bifurcation and Limit Cycle Analysis of the Rikitake System Xuedi Wang, Tianyu Yang, Wei Xu Nonlinear
More informationGeneralized-Type Synchronization of Hyperchaotic Oscillators Using a Vector Signal
Commun. Theor. Phys. (Beijing, China) 44 (25) pp. 72 78 c International Acaemic Publishers Vol. 44, No. 1, July 15, 25 Generalize-Type Synchronization of Hyperchaotic Oscillators Using a Vector Signal
More informationChaos synchronization of complex Rössler system
Appl. Math. Inf. Sci. 7, No. 4, 1415-1420 (2013) 1415 Applied Mathematics & Information Sciences An International Journal http://dx.doi.org/10.12785/amis/070420 Chaos synchronization of complex Rössler
More informationA New Hyperchaotic Attractor with Complex Patterns
A New Hyperchaotic Attractor with Complex Patterns Safieddine Bouali University of Tunis, Management Institute, Department of Quantitative Methods & Economics, 41, rue de la Liberté, 2000, Le Bardo, Tunisia
More informationFinite-time hybrid synchronization of time-delay hyperchaotic Lorenz system
ISSN 1746-7659 England UK Journal of Information and Computing Science Vol. 10 No. 4 2015 pp. 265-270 Finite-time hybrid synchronization of time-delay hyperchaotic Lorenz system Haijuan Chen 1 * Rui Chen
More informationADAPTIVE CONTROL AND SYNCHRONIZATION OF HYPERCHAOTIC NEWTON-LEIPNIK SYSTEM
ADAPTIVE CONTROL AND SYNCHRONIZATION OF HYPERCHAOTIC NEWTON-LEIPNIK SYSTEM Sundarapandian Vaidyanathan 1 1 Research and Development Centre, Vel Tech Dr. RR & Dr. SR Technical University Avadi, Chennai-600
More informationHopf bifurcations in an extended Lorenz system
Zhou et al. Advances in Difference Equations 2017 2017:28 DOI 10.1186/s13662-017-1083-8 R E S E A R C H Open Access Hopf ifurcations in an extended Lorenz system Zhiming Zhou 1,2*, Gheorghe Tigan 3 and
More informationCONTROLLING IN BETWEEN THE LORENZ AND THE CHEN SYSTEMS
International Journal of Bifurcation and Chaos, Vol. 12, No. 6 (22) 1417 1422 c World Scientific Publishing Company CONTROLLING IN BETWEEN THE LORENZ AND THE CHEN SYSTEMS JINHU LÜ Institute of Systems
More informationTime-delay feedback control in a delayed dynamical chaos system and its applications
Time-delay feedback control in a delayed dynamical chaos system and its applications Ye Zhi-Yong( ), Yang Guang( ), and Deng Cun-Bing( ) School of Mathematics and Physics, Chongqing University of Technology,
More informationLag anti-synchronization of delay coupled chaotic systems via a scalar signal
Lag anti-synchronization of delay coupled chaotic systems via a scalar signal Mohammad Ali Khan Abstract. In this letter, a chaotic anti-synchronization (AS scheme is proposed based on combining a nonlinear
More informationGeneralized projective synchronization of a class of chaotic (hyperchaotic) systems with uncertain parameters
Vol 16 No 5, May 2007 c 2007 Chin. Phys. Soc. 1009-1963/2007/16(05)/1246-06 Chinese Physics and IOP Publishing Ltd Generalized projective synchronization of a class of chaotic (hyperchaotic) systems with
More informationA Generalized Anti-synchronization of Discrete Chaotic Maps via Linear Transformations
ISSN 749-3889 (print), 749-3897 (online) International Journal of Nonlinear Science Vol.24(27) No., pp.44-52 A Generalized Anti-synchronization of Discrete Chaotic Maps via Linear Transformations Debjani
More informationInternational Journal of PharmTech Research CODEN (USA): IJPRIF, ISSN: Vol.8, No.3, pp , 2015
International Journal of PharmTech Research CODEN (USA): IJPRIF, ISSN: 0974-4304 Vol.8, No.3, pp 377-382, 2015 Adaptive Control of a Chemical Chaotic Reactor Sundarapandian Vaidyanathan* R & D Centre,Vel
More informationHomotopy Perturbation Method for the Fisher s Equation and Its Generalized
ISSN 749-889 (print), 749-897 (online) International Journal of Nonlinear Science Vol.8(2009) No.4,pp.448-455 Homotopy Perturbation Method for the Fisher s Equation and Its Generalized M. Matinfar,M. Ghanbari
More informationAdaptive feedback synchronization of a unified chaotic system
Physics Letters A 39 (4) 37 333 www.elsevier.com/locate/pla Adaptive feedback synchronization of a unified chaotic system Junan Lu a, Xiaoqun Wu a, Xiuping Han a, Jinhu Lü b, a School of Mathematics and
More informationBidirectional Partial Generalized Synchronization in Chaotic and Hyperchaotic Systems via a New Scheme
Commun. Theor. Phys. (Beijing, China) 45 (2006) pp. 1049 1056 c International Academic Publishers Vol. 45, No. 6, June 15, 2006 Bidirectional Partial Generalized Synchronization in Chaotic and Hyperchaotic
More informationA Novel Three Dimension Autonomous Chaotic System with a Quadratic Exponential Nonlinear Term
ETASR - Engineering, Technology & Applied Science Research Vol., o.,, 9-5 9 A Novel Three Dimension Autonomous Chaotic System with a Quadratic Exponential Nonlinear Term Fei Yu College of Information Science
More informationADAPTIVE CONTROL AND SYNCHRONIZATION OF A GENERALIZED LOTKA-VOLTERRA SYSTEM
ADAPTIVE CONTROL AND SYNCHRONIZATION OF A GENERALIZED LOTKA-VOLTERRA SYSTEM Sundarapandian Vaidyanathan 1 1 Research and Development Centre, Vel Tech Dr. RR & Dr. SR Technical University Avadi, Chennai-600
More informationChaotic Attractor With Bounded Function
Proceedings of Engineering & Technology (PET) Copyright IPCO-2016 pp. 880-886 Chaotic Attractor With Bounded Function Nahed Aouf Souayed Electronical and micro-electronical laboratory, Faculty of science
More informationADAPTIVE STABILIZATION AND SYNCHRONIZATION OF HYPERCHAOTIC QI SYSTEM
ADAPTIVE STABILIZATION AND SYNCHRONIZATION OF HYPERCHAOTIC QI SYSTEM Sundarapandian Vaidyanathan 1 1 Research and Development Centre, Vel Tech Dr. RR Dr. SR Technical University Avadi, Chennai-600 062,
More informationStudy on Proportional Synchronization of Hyperchaotic Circuit System
Commun. Theor. Phys. (Beijing, China) 43 (25) pp. 671 676 c International Academic Publishers Vol. 43, No. 4, April 15, 25 Study on Proportional Synchronization of Hyperchaotic Circuit System JIANG De-Ping,
More informationADAPTIVE CHAOS SYNCHRONIZATION OF UNCERTAIN HYPERCHAOTIC LORENZ AND HYPERCHAOTIC LÜ SYSTEMS
ADAPTIVE CHAOS SYNCHRONIZATION OF UNCERTAIN HYPERCHAOTIC LORENZ AND HYPERCHAOTIC LÜ SYSTEMS Sundarapandian Vaidyanathan 1 1 Research and Development Centre, Vel Tech Dr. RR & Dr. SR Technical University
More informationComputers and Mathematics with Applications. Adaptive anti-synchronization of chaotic systems with fully unknown parameters
Computers and Mathematics with Applications 59 (21) 3234 3244 Contents lists available at ScienceDirect Computers and Mathematics with Applications journal homepage: www.elsevier.com/locate/camwa Adaptive
More informationExperimental and numerical realization of higher order autonomous Van der Pol-Duffing oscillator
Indian Journal of Pure & Applied Physics Vol. 47, November 2009, pp. 823-827 Experimental and numerical realization of higher order autonomous Van der Pol-Duffing oscillator V Balachandran, * & G Kandiban
More informationANTI-SYNCHRONIZATON OF TWO DIFFERENT HYPERCHAOTIC SYSTEMS VIA ACTIVE GENERALIZED BACKSTEPPING METHOD
ANTI-SYNCHRONIZATON OF TWO DIFFERENT HYPERCHAOTIC SYSTEMS VIA ACTIVE GENERALIZED BACKSTEPPING METHOD Ali Reza Sahab 1 and Masoud Taleb Ziabari 1 Faculty of Engineering, Electrical Engineering Group, Islamic
More informationMULTISTABILITY IN A BUTTERFLY FLOW
International Journal of Bifurcation and Chaos, Vol. 23, No. 12 (2013) 1350199 (10 pages) c World Scientific Publishing Company DOI: 10.1142/S021812741350199X MULTISTABILITY IN A BUTTERFLY FLOW CHUNBIAO
More informationChaos Control of the Chaotic Symmetric Gyroscope System
48 Chaos Control of the Chaotic Symmetric Gyroscope System * Barış CEVHER, Yılmaz UYAROĞLU and 3 Selçuk EMIROĞLU,,3 Faculty of Engineering, Department of Electrical and Electronics Engineering Sakarya
More informationBackstepping synchronization of uncertain chaotic systems by a single driving variable
Vol 17 No 2, February 2008 c 2008 Chin. Phys. Soc. 1674-1056/2008/17(02)/0498-05 Chinese Physics B and IOP Publishing Ltd Backstepping synchronization of uncertain chaotic systems by a single driving variable
More informationADAPTIVE SYNCHRONIZATION FOR RÖSSLER AND CHUA S CIRCUIT SYSTEMS
Letters International Journal of Bifurcation and Chaos, Vol. 12, No. 7 (2002) 1579 1597 c World Scientific Publishing Company ADAPTIVE SYNCHRONIZATION FOR RÖSSLER AND CHUA S CIRCUIT SYSTEMS A. S. HEGAZI,H.N.AGIZA
More informationHopf Bifurcation Analysis and Approximation of Limit Cycle in Coupled Van Der Pol and Duffing Oscillators
The Open Acoustics Journal 8 9-3 9 Open Access Hopf ifurcation Analysis and Approximation of Limit Cycle in Coupled Van Der Pol and Duffing Oscillators Jianping Cai *a and Jianhe Shen b a Department of
More informationStabilization of Higher Periodic Orbits of Discrete-time Chaotic Systems
ISSN 749-3889 (print), 749-3897 (online) International Journal of Nonlinear Science Vol.4(27) No.2,pp.8-26 Stabilization of Higher Periodic Orbits of Discrete-time Chaotic Systems Guoliang Cai, Weihuai
More informationConstructing Chaotic Systems with Total Amplitude Control
International Journal of Bifurcation and Chaos, Vol. 25, No. 10 (2015) 1530025 (14 pages) c World Scientific Publishing Company DOI: 10.1142/S0218127415300256 Constructing Chaotic Systems with Total Amplitude
More informationADAPTIVE CHAOS CONTROL AND SYNCHRONIZATION OF HYPERCHAOTIC LIU SYSTEM
International Journal o Computer Science, Engineering and Inormation Technology (IJCSEIT), Vol.1, No., June 011 ADAPTIVE CHAOS CONTROL AND SYNCHRONIZATION OF HYPERCHAOTIC LIU SYSTEM Sundarapandian Vaidyanathan
More informationRecent new examples of hidden attractors
Eur. Phys. J. Special Topics 224, 1469 1476 (2015) EDP Sciences, Springer-Verlag 2015 DOI: 10.1140/epjst/e2015-02472-1 THE EUROPEAN PHYSICAL JOURNAL SPECIAL TOPICS Review Recent new examples of hidden
More informationSome explicit formulas of Lyapunov exponents for 3D quadratic mappings
Some explicit formulas of Lyapunov exponents for 3D quadratic mappings Zeraoulia Elhadj 1,J.C.Sprott 2 1 Department of Mathematics, University of Tébessa, (12002), Algeria. E-mail: zeraoulia@mail.univ-tebessa.dz
More informationSynchronizing Chaotic Systems Based on Tridiagonal Structure
Proceedings of the 7th World Congress The International Federation of Automatic Control Seoul, Korea, July 6-, 008 Synchronizing Chaotic Systems Based on Tridiagonal Structure Bin Liu, Min Jiang Zengke
More informationBIFURCATIONS AND SYNCHRONIZATION OF THE FRACTIONAL-ORDER SIMPLIFIED LORENZ HYPERCHAOTIC SYSTEM
Journal of Applied Analysis and Computation Volume 5, Number 2, May 215, 21 219 Website:http://jaac-online.com/ doi:1.11948/21519 BIFURCATIONS AND SYNCHRONIZATION OF THE FRACTIONAL-ORDER SIMPLIFIED LORENZ
More informationControlling a Novel Chaotic Attractor using Linear Feedback
ISSN 746-7659, England, UK Journal of Information and Computing Science Vol 5, No,, pp 7-4 Controlling a Novel Chaotic Attractor using Linear Feedback Lin Pan,, Daoyun Xu 3, and Wuneng Zhou College of
More informationFunction Projective Synchronization of Discrete-Time Chaotic and Hyperchaotic Systems Using Backstepping Method
Commun. Theor. Phys. (Beijing, China) 50 (2008) pp. 111 116 c Chinese Physical Society Vol. 50, No. 1, July 15, 2008 Function Projective Synchronization of Discrete-Time Chaotic and Hyperchaotic Systems
More informationA SYSTEMATIC PROCEDURE FOR SYNCHRONIZING HYPERCHAOS VIA OBSERVER DESIGN
Journal of Circuits, Systems, and Computers, Vol. 11, No. 1 (22) 1 16 c World Scientific Publishing Company A SYSTEMATIC PROCEDURE FOR SYNCHRONIZING HYPERCHAOS VIA OBSERVER DESIGN GIUSEPPE GRASSI Dipartimento
More informationCoexisting Hidden Attractors in a 4-D Simplified Lorenz System
International Journal of Bifurcation and Chaos, Vol. 24, No. 3 (2014) 1450034 (12 pages) c World Scientific Publishing Company DOI: 10.1142/S0218127414500345 Coexisting Hidden Attractors in a 4-D Simplified
More informationBifurcation Analysis, Chaos and Control in the Burgers Mapping
ISSN 1749-3889 print, 1749-3897 online International Journal of Nonlinear Science Vol.4007 No.3,pp.171-185 Bifurcation Analysis, Chaos and Control in the Burgers Mapping E. M. ELabbasy, H. N. Agiza, H.
More informationGuangyong Zhang a,, Lixin Tian a,b. (Received 12 November 2016, accepted 10 January 2017, )
ISSN 1749-3889 (print), 1749-3897 (online) International Journal of Nonlinear Science Vol.23(217) No.2, pp.19-115 Evolution Analysis and Application of the Dynamic System Based on Energy Prices-Energy
More information698 Zou Yan-Li et al Vol. 14 and L 2, respectively, V 0 is the forward voltage drop across the diode, and H(u) is the Heaviside function 8 < 0 u < 0;
Vol 14 No 4, April 2005 cfl 2005 Chin. Phys. Soc. 1009-1963/2005/14(04)/0697-06 Chinese Physics and IOP Publishing Ltd Chaotic coupling synchronization of hyperchaotic oscillators * Zou Yan-Li( ΠΛ) a)y,
More informationADAPTIVE DESIGN OF CONTROLLER AND SYNCHRONIZER FOR LU-XIAO CHAOTIC SYSTEM
ADAPTIVE DESIGN OF CONTROLLER AND SYNCHRONIZER FOR LU-XIAO CHAOTIC SYSTEM WITH UNKNOWN PARAMETERS Sundarapandian Vaidyanathan 1 1 Research and Development Centre, Vel Tech Dr. RR & Dr. SR Technical University
More informationADAPTIVE CONTROLLER DESIGN FOR THE ANTI-SYNCHRONIZATION OF HYPERCHAOTIC YANG AND HYPERCHAOTIC PANG SYSTEMS
ADAPTIVE CONTROLLER DESIGN FOR THE ANTI-SYNCHRONIZATION OF HYPERCHAOTIC YANG AND HYPERCHAOTIC PANG SYSTEMS Sundarapandian Vaidyanathan 1 1 Research and Development Centre, Vel Tech Dr. RR & Dr. SR Technical
More informationA new four-dimensional chaotic system
Chin. Phys. B Vol. 19 No. 12 2010) 120510 A new four-imensional chaotic system Chen Yong ) a)b) an Yang Yun-Qing ) a) a) Shanghai Key Laboratory of Trustworthy Computing East China Normal University Shanghai
More informationBifurcation control and chaos in a linear impulsive system
Vol 8 No 2, December 2009 c 2009 Chin. Phys. Soc. 674-056/2009/82)/5235-07 Chinese Physics B and IOP Publishing Ltd Bifurcation control and chaos in a linear impulsive system Jiang Gui-Rong 蒋贵荣 ) a)b),
More informationADAPTIVE FEEDBACK LINEARIZING CONTROL OF CHUA S CIRCUIT
International Journal of Bifurcation and Chaos, Vol. 12, No. 7 (2002) 1599 1604 c World Scientific Publishing Company ADAPTIVE FEEDBACK LINEARIZING CONTROL OF CHUA S CIRCUIT KEVIN BARONE and SAHJENDRA
More informationA New Fractional-Order Chaotic System and Its Synchronization with Circuit Simulation
Circuits Syst Signal Process (2012) 31:1599 1613 DOI 10.1007/s00034-012-9408-z A New Fractional-Order Chaotic System and Its Synchronization with Circuit Simulation Diyi Chen Chengfu Liu Cong Wu Yongjian
More informationGeneralized projective synchronization between two chaotic gyros with nonlinear damping
Generalized projective synchronization between two chaotic gyros with nonlinear damping Min Fu-Hong( ) Department of Electrical and Automation Engineering, Nanjing Normal University, Nanjing 210042, China
More informationConstructing a chaotic system with any number of equilibria
Nonlinear Dyn (2013) 71:429 436 DOI 10.1007/s11071-012-0669-7 ORIGINAL PAPER Constructing a chaotic system with any number of equilibria Xiong Wang Guanrong Chen Received: 9 June 2012 / Accepted: 29 October
More informationParametric convergence and control of chaotic system using adaptive feedback linearization
Available online at www.sciencedirect.com Chaos, Solitons and Fractals 4 (29) 1475 1483 www.elsevier.com/locate/chaos Parametric convergence and control of chaotic system using adaptive feedback linearization
More informationMULTI-SCROLL CHAOTIC AND HYPERCHAOTIC ATTRACTORS GENERATED FROM CHEN SYSTEM
International Journal of Bifurcation and Chaos, Vol. 22, No. 2 (212) 133 ( pages) c World Scientific Publishing Compan DOI: 1.1142/S21812741332 MULTI-SCROLL CHAOTIC AND HYPERCHAOTIC ATTRACTORS GENERATED
More informationGeneralized Function Projective Lag Synchronization in Fractional-Order Chaotic Systems
Generalized Function Projective Lag Synchronization in Fractional-Order Chaotic Systems Yancheng Ma Guoan Wu and Lan Jiang denotes fractional order of drive system Abstract In this paper a new synchronization
More informationTravelling Wave Solutions for the Gilson-Pickering Equation by Using the Simplified G /G-expansion Method
ISSN 1749-3889 (print, 1749-3897 (online International Journal of Nonlinear Science Vol8(009 No3,pp368-373 Travelling Wave Solutions for the ilson-pickering Equation by Using the Simplified /-expansion
More informationCrisis in Amplitude Control Hides in Multistability
International Journal of Bifurcation and Chaos, Vol. 26, No. 14 (2016) 1650233 (11 pages) c World Scientific Publishing Company DOI: 10.1142/S0218127416502333 Crisis in Amplitude Control Hides in Multistability
More informationA Unified Lorenz-Like System and Its Tracking Control
Commun. Theor. Phys. 63 (2015) 317 324 Vol. 63, No. 3, March 1, 2015 A Unified Lorenz-Like System and Its Tracking Control LI Chun-Lai ( ) 1, and ZHAO Yi-Bo ( ) 2,3 1 College of Physics and Electronics,
More informationEQUILIBRIA AND STABILITY ANALYSIS OF A BRANCHED METABOLIC NETWORK WITH FEEDBACK INHIBITION. F. Grognard Y. Chitour G. Bastin
EQUILIBRIA AND STABILITY ANALYSIS OF A BRANCHED METABOLIC NETWORK WITH FEEDBACK INHIBITION F. Grognard Y. Chitour G. Bastin Projet COMORE. INRIA Sophia-Antipolis. BP 93 06902 Sophia-Antipolis Cedex, France
More informationChaos synchronization of nonlinear Bloch equations
Chaos, Solitons and Fractal7 (26) 357 361 www.elsevier.com/locate/chaos Chaos synchronization of nonlinear Bloch equations Ju H. Park * Robust Control and Nonlinear Dynamics Laboratory, Department of Electrical
More informationChaotifying 2-D piecewise linear maps via a piecewise linear controller function
Chaotifying 2-D piecewise linear maps via a piecewise linear controller function Zeraoulia Elhadj 1,J.C.Sprott 2 1 Department of Mathematics, University of Tébéssa, (12000), Algeria. E-mail: zeraoulia@mail.univ-tebessa.dz
More informationFunction Projective Synchronization of Fractional-Order Hyperchaotic System Based on Open-Plus-Closed-Looping
Commun. Theor. Phys. 55 (2011) 617 621 Vol. 55, No. 4, April 15, 2011 Function Projective Synchronization of Fractional-Order Hyperchaotic System Based on Open-Plus-Closed-Looping WANG Xing-Yuan ( ), LIU
More informationConstruction of a New Fractional Chaotic System and Generalized Synchronization
Commun. Theor. Phys. (Beijing, China) 5 (2010) pp. 1105 1110 c Chinese Physical Society and IOP Publishing Ltd Vol. 5, No. 6, June 15, 2010 Construction of a New Fractional Chaotic System and Generalized
More informationCompacton Solutions and Peakon Solutions for a Coupled Nonlinear Wave Equation
ISSN 1749-3889 (print), 1749-3897 (online) International Journal of Nonlinear Science Vol 4(007) No1,pp31-36 Compacton Solutions Peakon Solutions for a Coupled Nonlinear Wave Equation Dianchen Lu, Guangjuan
More informationControlling chaos in Colpitts oscillator
Chaos, Solitons and Fractals 33 (2007) 582 587 www.elsevier.com/locate/chaos Controlling chaos in Colpitts oscillator Guo Hui Li a, *, Shi Ping Zhou b, Kui Yang b a Department of Communication Engineering,
More informationNumerical Simulation of the Generalized Hirota-Satsuma Coupled KdV Equations by Variational Iteration Method
ISSN 1749-3889 (print), 1749-3897 (online) International Journal of Nonlinear Science Vol.7(29) No.1,pp.67-74 Numerical Simulation of the Generalized Hirota-Satsuma Coupled KdV Equations by Variational
More informationFlat Chain and Flat Cochain Related to Koch Curve
ISSN 1479-3889 (print), 1479-3897 (online) International Journal of Nonlinear Science Vol. 3 (2007) No. 2, pp. 144-149 Flat Chain and Flat Cochain Related to Koch Curve Lifeng Xi Institute of Mathematics,
More informationA NEW CHAOTIC SYSTEM AND BEYOND: THE GENERALIZED LORENZ-LIKE SYSTEM
Tutorials and Reviews International Journal of Bifurcation and Chaos, Vol. 14, No. 4) 17 17 c World Scientific Pulishing Compan A NEW CHAOTIC SYSTEM AND BEYOND: THE GENERALIZED LORENZ-LIKE SYSTEM JINHU
More informationAnalysis of Duopoly Output Game With Different Decision-Making Rules
Management Science and Engineering Vol. 9, No. 1, 015, pp. 19-4 DOI: 10.3968/6117 ISSN 1913-0341 [Print] ISSN 1913-035X [Online] www.cscanada.net www.cscanada.org Analysis of Duopoly Output Game With Different
More informationSynchronization of different chaotic systems and electronic circuit analysis
Synchronization of different chaotic systems and electronic circuit analysis J.. Park, T.. Lee,.. Ji,.. Jung, S.M. Lee epartment of lectrical ngineering, eungnam University, Kyongsan, Republic of Korea.
More informationKingSaudBinAbdulazizUniversityforHealthScience,Riyadh11481,SaudiArabia. Correspondence should be addressed to Raghib Abu-Saris;
Chaos Volume 26, Article ID 49252, 7 pages http://dx.doi.org/.55/26/49252 Research Article On Matrix Projective Synchronization and Inverse Matrix Projective Synchronization for Different and Identical
More informationA Generalization of Some Lag Synchronization of System with Parabolic Partial Differential Equation
American Journal of Theoretical and Applied Statistics 2017; 6(5-1): 8-12 http://www.sciencepublishinggroup.com/j/ajtas doi: 10.11648/j.ajtas.s.2017060501.12 ISSN: 2326-8999 (Print); ISSN: 2326-9006 (Online)
More informationGLOBAL CHAOS SYNCHRONIZATION OF UNCERTAIN SPROTT J AND K SYSTEMS BY ADAPTIVE CONTROL
GLOBAL CHAOS SYNCHRONIZATION OF UNCERTAIN SPROTT J AND K SYSTEMS BY ADAPTIVE CONTROL Sundarapandian Vaidyanathan 1 1 Research and Development Centre, Vel Tech Dr. RR & Dr. SR Technical University Avadi,
More informationFUZZY CONTROL OF CHAOS
International Journal of Bifurcation and Chaos, Vol. 8, No. 8 (1998) 1743 1747 c World Scientific Publishing Company FUZZY CONTROL OF CHAOS OSCAR CALVO CICpBA, L.E.I.C.I., Departamento de Electrotecnia,
More informationRobust Gain Scheduling Synchronization Method for Quadratic Chaotic Systems With Channel Time Delay Yu Liang and Horacio J.
604 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I: REGULAR PAPERS, VOL. 56, NO. 3, MARCH 2009 Robust Gain Scheduling Synchronization Method for Quadratic Chaotic Systems With Channel Time Delay Yu Liang
More informationFUZZY CONTROL OF CHAOS
FUZZY CONTROL OF CHAOS OSCAR CALVO, CICpBA, L.E.I.C.I., Departamento de Electrotecnia, Facultad de Ingeniería, Universidad Nacional de La Plata, 1900 La Plata, Argentina JULYAN H. E. CARTWRIGHT, Departament
More informationDynamics at infinity and a Hopf bifurcation arising in a quadratic system with coexisting attractors
Pramana J. Phys. 8) 9: https://doi.org/.7/s43-7-55-x Indian Academy of Sciences Dynamics at infinity and a Hopf bifurcation arising in a quadratic system with coexisting attractors ZHEN WANG,,,IRENEMOROZ
More informationTracking the State of the Hindmarsh-Rose Neuron by Using the Coullet Chaotic System Based on a Single Input
ISSN 1746-7659, England, UK Journal of Information and Computing Science Vol. 11, No., 016, pp.083-09 Tracking the State of the Hindmarsh-Rose Neuron by Using the Coullet Chaotic System Based on a Single
More information