Application Research of Fireworks Algorithm in Parameter Estimation for Chaotic System
|
|
- Juliana Marshall
- 5 years ago
- Views:
Transcription
1 Application Research of Fireworks Algorithm in Parameter Estimation for Chaotic System Hao Li 1,3, Ying Tan 2, Jun-Jie Xue 1 and Jie Zhu 1 1 Air Force Engineering University, Xi an, , China 2 Department of Machine Intelligence, School of Electronics Engineering and Computer Science, Peking University, Beijing, , China 3 Department of Intelligence, Air Force Early-Warning Academy, Wuhan, , China Abstract. Chaotic system is a nonlinear deterministic system, and parameter identification for chaotic system is an important issue in nonlinear science, such as secure communication, et al. By set up appropriate objective function, the parameter identification can be converted into a multi-dimensional optimization problem which can be solved by evolutionary algorithms. Emerging as an evolutionary algorithm, Fireworks Algorithm () has shown its good computational performance and robustness. In order to expand the application of, several types of are applied to estimate the parameters for two typical chaotic system which three parameters are totally unknown, simulation results show most s can attain better estimation precision and robustness, is a new effective parameter identification method for chaotic systems. 1 Introduction Chaos embodies characteristics including complexity, internal randomness, initial value sensitivity, irregular order and so on [1]. In scientific research and engineering application, chaotic characteristics is presented in various systems and therefore chaotic system s control and synchronization have become an important research field and also widely applied in fields such as secure communication, medicine, biography and chemistry [2]. Many nonlinear system control methods like adaptive control [3], active control [4] and PI control [5] can be used in chaotic system s control and synchronization. However, if parameters of chaotic system are unknown, all of these methods above are not applicable anymore. In engineering practice, there exist some unknown parameters caused by chaotic system s complexity making some parameters hard to measure or communication security [6]. Consequently, parameter estimation of chaotic system becomes a key issue in chaotic control and synchronization. Essentially, parameter estimation of chaotic system is an optimization problem for multi-dimensional complex function. Intelligent optimization algorithms have widely applied in resolving such kind of problems. In reference [7], genetic algorithm (GA) was used for single parameter estimation of Lorenz system, achieved better results but slower convergence, Single parameter s estimation performance of ant colony algorithm for chaotic system has been studied in
2 2 Manuscript for The Sixth International Conference on Swarm Intelligence 2015 both noisy and non-noisy backgrounds in reference [8], but as its text spoken ant colony algorithm for chaotic parameter estimation also had slow convergence problem. Based on opposition-based learning and harmony search algorithm, a hybrid biogeography-based optimization (HBBO) is proposed in reference [9] and achieve better results of both Lorenz system and Rossler system, In addition, adaptive spatial contraction bee colony algorithm [10], chaotic invasive weed optimization [11], cuckoo adaptive search, simulated annealing hybrid algorithm [12], oppositional seeker optimization algorithm [13] and other algorithms are also used for parameter estimation of chaotic systems. However, according to the famous No Free Lunch Theorems that was proposed by Wolpert and Macready in 1997, there doesn t exist one method that can solve all kinds of problems. Therefore, different parameter estimation method should be developed aiming at specific problem [14]. The Fireworks Algorithm () is a newly developed evolutionary algorithm that was published by Tan and Zhu in 2010 (Tan, & Zhu, 2010) [15]. Like other evolution algorithms, it also aims to find the vector with the best (usually minimum) fitness in the search space. It is inspired by fireworks explosion at night and is quite effective at finding global optimal value. As a firework explodes, a shower of sparks is shown in the adjacent area. Those sparks will explode again and generate other shows of sparks in a smaller area. Gradually, the sparks will search the whole solution space in a fine structure and focus on a small place to find the optimal solution. It has favorable global search ability as well as computational robustness [16]. Therefore we use several types of for parameter estimation of two typical chaotic system. Experiments show that the method has better adaptability, reliability and high precision. It is proved to be a successful approach in parameter estimation for chaotic systems. 2 Fireworks Algorithm 2.1 Framework Assume that the number of fireworks is N and the number of dimensions is d, then the explosion amplitude A (Eq. 1) and the number of explosion sparks s (Eq. 2) for each firework X i are calculated as follows: A i = Â f(x i ) y min + ε N i=1 (f(x i) y min ) + ε. (1) s i = M e y max f(x i ) + ε N i=1 (y max f(x i )) + ε. (2) where y max = max(f(x i )), y min = min(f(x i )), Â and M e are two constants to control the explosion amplitude and the number of explosion sparks, respectively, and ε is the machine epsilon. To avoid the overwhelming effects of fireworks at
3 Manuscript for The Sixth International Conference on Swarm Intelligence good locations, the number of sparks is bounded by: round(am e ) if s i < am e, s i = round(bm e ) if s i > bm e, round(s i ) otherwise. (3) where a and b are constant parameters that confine the range of the population size. Based on A i and s i, the explosion operator is performed. For each of the s i explosion sparks of each firework X i, Algorithm 1 is performed once. In Line 7 of Algorithm 1, the operator % refers to the modulo operation (remainder of division), and X k min and Xk max refer to the lower and upper bounds of the search space in dimension k. Algorithm 1 Generating explosion sparks in 1: Initialize the location of the explosion sparks: ˆX i = X i 2: Calculate offset displacement: X = A i rand( 1, 1) 3: Set z k = round(d rand(0, 1)), k = 1, 2,..., d 4: for each dimension of ˆ Xk i {z k dimensions of ˆX i } do 5: ˆ Xk i 6: if ˆ Xk i 7: ˆ Xk i 8: end if 9: end for = X ˆ i k + X out of bounds then = Xmin k + X ˆ i k %(Xk max Xmin) k After the explosion, another type of sparks, the Gaussian sparks, are generated based on a Gaussian mutation process. This algorithm is performed M g times, each time with a randomly selected firework X i (M g is a constant to control the number of Gaussian sparks). Algorithm 2 Generating Gaussian sparks in 1: Initialize the location of the Gaussian sparks: X i = X i 2: Calculate offset displacement: e = Gaussian(1, 1) 3: Set z k = round(d rand(0, 1)), k = 1, 2,..., d 4: for each dimension of Xk i {z k dimensions of X i} do 5: Xk i 6: if Xk i 7: Xk i 8: end if 9: end for = X i k e out of bounds then = Xmin k + X i k %(Xk max Xmin) k In order to retain the information and pass it to the next generation, a new population of fireworks is selected at the end of each iteration. All original fireworks, as well as all explosion and Gaussian sparks can be selected for the next iteration (in total, N fireworks/sparks are selected). selected based on a distance based selection operator. For location X i, the selection probability p i is calculated by: R(X i ) p(x i ) = j K R(X j). (4)
4 4 Manuscript for The Sixth International Conference on Swarm Intelligence 2015 R(X i ) = j K d(x i, X j ) = j K X i X j. (5) where K is the set of all current locations including original fireworks and both types of sparks (without the best location). As a result, fireworks or sparks in low crowded regions will have a higher probability to be selected for the next iteration than fireworks or sparks in crowded regions. N individuals choose as the next iteration of the fireworks from the fireworks, explosion sparks and Gaussian sparks population, return optimization results. This cycle is repeated until you find the global optimal value. 2.2 Experiments To test the performance of the proposed, we conducted experiments on nine benchmark functions. The expression of the functions, initialization intervals and dimensions are listed blew: Table 1. Nine benchmark functions Function Expression Initialization D Sphere F 1 = D i=1 x2 i [30, 50] D 30 Rosenbrock F 2 = ( D 1 100(xi+1 x 2 i=1 i ) 2 + (x i 1) 2) [30, 50] D 30 Rastrigrin F 3 = ( D i=1 x 2 i 10cos(2πx i ) + 10 ) [30, 50] D 30 Griewank F 4 = 1 + D (x 2 i ) D cos( x i i= i=1 i ) [30, 50] D 30 Ellipse F 5 = i 1 D 104 D 1 x 2 i=1 i [15, 30] D 30 Cigar F 6 = x D i=2 104 x 2 i [15, 30] D 30 Tablet F 7 = 10 4 x D i=2 x2 i [15, 30] D 30 Schwefel F 8 = ( D (x1 x 2 i=1 i ) 2 + (x i 1) 2) [15, 30] D 30 ( ) 1 D F 9 = 20 + e 20exp 0.2 D i=1 Ackley x2 i [15, 30] D 30 exp ( 1 D D i=1 cos(2πx2 i ) ) We compare the performance of the with the CPSO and the SPSO in terms of optimization accuracy. The parameters of both the CPSO and the SPSO are set as those in Ref. [17]. For the, the parameters are set as those in Ref. [15]: N = 5, M e = 50, a = 0.04, b = 0.8, Â = 40 and M g = 5, Table 2. are statistical mean and standard deviation of solutions found by the, the CPSO and the SPSO over 20 independent runs:
5 Manuscript for The Sixth International Conference on Swarm Intelligence Table 2. Statistical Results Function Function Mean CPSO Mean [15] SPSO Mean [15] evluations (StD) (StD) [15] (StD) [15] Sphere Rosenbrock Rastrigrin Griewank Ellipse Cigar Tablet Schwefel Ackley ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) According to Table 2, under the same standard, all the statistical mean and standard acquired by computing various complicated functions with are superior to that attained by other two algorithms. s outstanding global optimum searching ability and computation stability are both verified in experiments. 2.3 Extensions Fireworks algorithm works quite well on test functions. but there are still some places for improvement. Zheng et al. (Zheng, Janecek, & Tan, 2013) proposed an enhanced fireworks algorithm (E) in Ref [18], Zheng S proposed a dynamic search in fireworks algorithm (dyn) in Ref [19], and adaptive fireworks algorithm (A) is proposed by Li et al in 2014 [20]. In this paper, we will take advantage of these types of fireworks algorithm to estimate the parameters
6 6 Manuscript for The Sixth International Conference on Swarm Intelligence 2015 of chaotic systems. These algorithms are not specific elaborate in detail here, please refer to the relevant paper. 3 Estimation Framework of Chaotic System Generally speaking, an n-dimensional chaotic system could be expressed as follow formula: Ẋ = F (X, X 0, θ) (6) Where X = (x 1, x 2,..., x n ) T R n denotes n-dimensional state variable of original system, X 0 denotes system s initial state and θ = (θ 1, θ 2,..., θ m ) T R m is the unknown parameters vector, in the context that system structure is known, estimation system can be expressed as: Ẏ = F (Y, X 0, θ) (7) Where Y = (y 1, y 2,..., y n ) T R n denotes n-dimensional state variable of estimation system, and θ = ( θ 1, θ 2,..., θ m ) T R m denotes estimation values of parameters. Consequently, parameters estimation for chaotic system is transformed into an optimization problem as follow: min J( θ) = 1 M M X k Y k 2 (8) k=1 In the expression above, M denotes sequence length of state variables in parameter estimation; X k and Y k denote state variables at kth moment of the real system and estimation system respectively. Obviously, parameter estimation of chaotic system is equivalent to a multi-dimensional continuous optimization problem which needs to search for the optimum of decision variable θ to acquire minimum value of target function J( θ). Accordingly, the schematic diagram of chaotic system s parameter estimation is depicted in Fig. 1. X X F X X X X X M J best Y F Y X Y Y YM Fig. 1. The Flowchart of Chaotic Parameter Estimation
7 Manuscript for The Sixth International Conference on Swarm Intelligence Simulations and Analysis 4.1 Lorenz chaotic system Presented by Lorenz in 1963, can describe several different physical systems such as disk dynamos, laser devices and several problems related to convection [21]. Dynamic equation of Lorenz system is expressed as follow: ẋ = a(y x) ẏ = bx xz y ż = xy cz In which x, y and z represent state variables of system, a = 10, b = 28 and c = 8/3 are real parameter values. Using to estimate a, b and c in Lorenz. The initial range of estimated parameters is 9 a 11, 20 b 30 and 2 c 3. For the, the parameters are set as those: is 100 times, N = 5, M e = 50, a = 0.04, b = 0.8, Â = 40 and M g = 5. Table 3 are statistical optimums, mean and worst values of parameter estimation found by the, the E, the dyn, the A, the GA, the PSO and the BBO over 20 independent runs: Fig. 2 and Fig. 3 are the average fitness evolution curve of and convergence curves of parameter estimation after 20 times independent running. (9) E dyn A E dyn A Fitness Fitness(Log) Fig. 2. Average fitness evolution curve for Lorenz system
8 8 Manuscript for The Sixth International Conference on Swarm Intelligence 2015 Table 3. Results of parameter estimation for Lorenz system Fitness Algorithm a b c J GA [22] PSO [22] Optimums Averages Worst values BBO [9] E dyn A GA [22] PSO [22] BBO [9] E dyn A GA [22] PSO [22] BBO [9] E dyn A
9 Manuscript for The Sixth International Conference on Swarm Intelligence E dyn A a E dyn A b E dyn A c Fig. 3. Average parameter estimation curve of for Lorenz system According to Table 2, Fig. 2 and Fig. 3, Overall speaking, compared with other 3 algorithm, and its variants can get a better parameter estimation accuracy, specifically E and A, can be achieved In these types
10 10 Manuscript for The Sixth International Conference on Swarm Intelligence 2015 of fireworks algorithms, A has the fastest fitness convergence rate, E has the best fitness optimums and evolution curve. 4.2 Rossler chaotic system As a simplified model of a chemical reaction system [23], Rossler system s expression showed as below is also a very famous function in nonlinear dynamics: ẋ = y z ẏ = ay + x (10) ż = b + z(x c) Rossler parameters real values are set as a = 0.2, b = 0.4, c = 5.7. Search range of estimation parameters is [0, 10]. For the, the parameters are set as those: is 100 times, N = 5, M e = 10, a = 0.04, b = 0.8, Â = 40 and M g = 5 (in total, 20 fireworks/sparks). 5 times of independent parameter estimation of Rossler system have been processed with and simulation results are compared with results of HBBO in reference [9] and DE introduced in reference [24] in Table 4. The average fitness evolution curve of and convergence curves of parameter estimation are drawn in Figure 4 and Figure 5 respectively. It is show that s have a fast convergence speed as well as outstanding performance in global optimum searching according to Figure 4 and Figure 5. Simulation results outline both solving precision and computation stability of s E dyn A E dyn A Fitness Fitness(Log) Fig. 4. Average fitness evolution curve for Rossler system
11 Manuscript for The Sixth International Conference on Swarm Intelligence Table 4. Results of parameter estimation for Rossler system Fitness Algorithm a b c J DE [24] Optimums HBBO [9] E dyn A DE [24] Averages HBBO [9] E dyn A DE [24] Worst values HBBO [9] E dyn A
12 12 Manuscript for The Sixth International Conference on Swarm Intelligence E dyn A a b E dyn A E dyn A c Fig. 5. Average parameter estimation curve of for Rossler system
13 Manuscript for The Sixth International Conference on Swarm Intelligence Conclusion In this paper, chaotic system parameter estimation problem is transformed into a class of multi-dimensional parameter optimization problem. In order to expand the application of which emerging recently, was introduced, validated and finally applied to estimate the unknown parameters of chaotic systems. With Lorenz and Rossler chaotic system, the simulation results show that the can get better effect than other algorithms, it is a new and effective chaotic system parameter estimation method. 6 Acknowledgment This work is supported by National Natural Science Foundation of China under Grant No , No and References 1. Wang L, Xu Y: Expert. Syst. Appl. 38 (2011) Liu L Z, Zhang J Q, Xu G X, Liang L S, Wang M S: Acta Phys. Sin. 63 (2014) (in Chinese) 3. Hegazi A S, Agiza H N, Dessoky M M E: Internatinal Journal of Bifurcation and Chaos 12 (2002) Huang L L, Feng R P, Wang M: Physic Letters A 320 (2004) Cheng D L, Huang C F, Cheng S Y, Yan J J: Expert Systems with Applications 36 (2009) Liu Y, Wallace K S: Nonlinear. Dyn. 66 (2011) Dai D, Ma X Q, Li F C, You Y: Acta Phys. Sin. 51 (2002) Li L X, Peng H P, Yang Y X, Wang X D: Acta Phys. Sin. 56 (2007) Lin J, Xu L: Acta Phys. Sin. 62 (2013) Gao F, Fei F X, Xu Q, Deng Y Y, Qi Y B, Balasingham I: Applied Mathematics and Computation 219 (2012) Ahmadi M, Mojallali H: Chaos, Solitons & Fractals 45 (2012) Sheng Z, Wang J, Zhou S D, Zhou B H: CHAOS 24 (2014) Lin J, Chen Chang: Nonlinear. Dyn. 76 (2014) Wang L, He W P, Wang S Q, Liao L J, He T: Acta Phys. Sin. 63 (2014) Tan Y, Zhu Y: Fireworks algorithm for optimization Berlin: Springer (2010) Tan Y, Yu C, Zheng S Q: International Journal of Swarm Intelligence Research 4 (2013) Tan Y, Xiao Z M: Proceedings of IEEE Congress on Evolutionary Computation (2007) Zheng S, Janecik A, Tan Y: IEEE Congress on Evolutionary Computation (2013) Zheng S, Janecik A, Li J: IEEE Congress on Evolutionary Computation (2014) Li J, Zheng S, Tan Y: IEEE Congress on Evolutionary Computation (2014)
14 14 Manuscript for The Sixth International Conference on Swarm Intelligence Mahmoud G. M., Alkashif M. A., Aly S. A.: Int. J. Mod. Phys. C. 18 (2007) Kusum D, Manoj T: Appl. Math. Comput 188 (2007) Rossler O E: Physics Letters A 57 (1996) Ho W H, Chou C Y: Nonlinear. Dyn. 61 (2010) 29 41
Dynamic Search Fireworks Algorithm with Covariance Mutation for Solving the CEC 2015 Learning Based Competition Problems
Dynamic Search Fireworks Algorithm with Covariance Mutation for Solving the CEC 05 Learning Based Competition Problems Chao Yu, Ling Chen Kelley,, and Ying Tan, The Key Laboratory of Machine Perception
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 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 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 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 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 informationDynamical behaviour of a controlled vibro-impact system
Vol 17 No 7, July 2008 c 2008 Chin. Phys. Soc. 1674-1056/2008/17(07)/2446-05 Chinese Physics B and IOP Publishing Ltd Dynamical behaviour of a controlled vibro-impact system Wang Liang( ), Xu Wei( ), and
More informationBeta Damping Quantum Behaved Particle Swarm Optimization
Beta Damping Quantum Behaved Particle Swarm Optimization Tarek M. Elbarbary, Hesham A. Hefny, Atef abel Moneim Institute of Statistical Studies and Research, Cairo University, Giza, Egypt tareqbarbary@yahoo.com,
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 informationVerification of a hypothesis about unification and simplification for position updating formulas in particle swarm optimization.
nd Workshop on Advanced Research and Technology in Industry Applications (WARTIA ) Verification of a hypothesis about unification and simplification for position updating formulas in particle swarm optimization
More informationProjective synchronization of a complex network with different fractional order chaos nodes
Projective synchronization of a complex network with different fractional order chaos nodes Wang Ming-Jun( ) a)b), Wang Xing-Yuan( ) a), and Niu Yu-Jun( ) a) a) School of Electronic and Information Engineering,
More informationA 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 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 informationNo. 6 Determining the input dimension of a To model a nonlinear time series with the widely used feed-forward neural network means to fit the a
Vol 12 No 6, June 2003 cfl 2003 Chin. Phys. Soc. 1009-1963/2003/12(06)/0594-05 Chinese Physics and IOP Publishing Ltd Determining the input dimension of a neural network for nonlinear time series prediction
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 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 informationFuzzy adaptive catfish particle swarm optimization
ORIGINAL RESEARCH Fuzzy adaptive catfish particle swarm optimization Li-Yeh Chuang, Sheng-Wei Tsai, Cheng-Hong Yang. Institute of Biotechnology and Chemical Engineering, I-Shou University, Kaohsiung, Taiwan
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 informationResearch Article Design of PDC Controllers by Matrix Reversibility for Synchronization of Yin and Yang Chaotic Takagi-Sugeno Fuzzy Henon Maps
Abstract and Applied Analysis Volume 212, Article ID 35821, 11 pages doi:1.1155/212/35821 Research Article Design of PDC Controllers by Matrix Reversibility for Synchronization of Yin and Yang Chaotic
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 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 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 informationResearch Article A Novel Differential Evolution Invasive Weed Optimization Algorithm for Solving Nonlinear Equations Systems
Journal of Applied Mathematics Volume 2013, Article ID 757391, 18 pages http://dx.doi.org/10.1155/2013/757391 Research Article A Novel Differential Evolution Invasive Weed Optimization for Solving Nonlinear
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 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 informationNonlinear Controller Design of the Inverted Pendulum System based on Extended State Observer Limin Du, Fucheng Cao
International Conference on Automation, Mechanical Control and Computational Engineering (AMCCE 015) Nonlinear Controller Design of the Inverted Pendulum System based on Extended State Observer Limin Du,
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 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 self-guided Particle Swarm Optimization with Independent Dynamic Inertia Weights Setting on Each Particle
Appl. Math. Inf. Sci. 7, No. 2, 545-552 (2013) 545 Applied Mathematics & Information Sciences An International Journal A self-guided Particle Swarm Optimization with Independent Dynamic Inertia Weights
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 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 informationDouble-distance propagation of Gaussian beams passing through a tilted cat-eye optical lens in a turbulent atmosphere
Double-distance propagation of Gaussian beams passing through a tilted cat-eye optical lens in a turbulent atmosphere Zhao Yan-Zhong( ), Sun Hua-Yan( ), and Song Feng-Hua( ) Department of Photoelectric
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 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 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 informationPSO with Adaptive Mutation and Inertia Weight and Its Application in Parameter Estimation of Dynamic Systems
Vol. 37, No. 5 ACTA AUTOMATICA SINICA May, 2011 PSO with Adaptive Mutation and Inertia Weight and Its Application in Parameter Estimation of Dynamic Systems ALFI Alireza 1 Abstract An important problem
More informationFour-dimensional hyperchaotic system and application research in signal encryption
16 3 2012 3 ELECTRI C MACHINES AND CONTROL Vol. 16 No. 3 Mar. 2012 1 2 1 1. 150080 2. 150080 Lyapunov TP 273 A 1007-449X 2012 03-0096- 05 Four-dimensional hyperchaotic system and application research in
More informationON THE USE OF RANDOM VARIABLES IN PARTICLE SWARM OPTIMIZATIONS: A COMPARATIVE STUDY OF GAUSSIAN AND UNIFORM DISTRIBUTIONS
J. of Electromagn. Waves and Appl., Vol. 23, 711 721, 2009 ON THE USE OF RANDOM VARIABLES IN PARTICLE SWARM OPTIMIZATIONS: A COMPARATIVE STUDY OF GAUSSIAN AND UNIFORM DISTRIBUTIONS L. Zhang, F. Yang, and
More informationNew Homoclinic and Heteroclinic Solutions for Zakharov System
Commun. Theor. Phys. 58 (2012) 749 753 Vol. 58, No. 5, November 15, 2012 New Homoclinic and Heteroclinic Solutions for Zakharov System WANG Chuan-Jian ( ), 1 DAI Zheng-De (à ), 2, and MU Gui (½ ) 3 1 Department
More informationChaos suppression of uncertain gyros in a given finite time
Chin. Phys. B Vol. 1, No. 11 1 1155 Chaos suppression of uncertain gyros in a given finite time Mohammad Pourmahmood Aghababa a and Hasan Pourmahmood Aghababa bc a Electrical Engineering Department, Urmia
More informationEvolutionary Programming Using a Mixed Strategy Adapting to Local Fitness Landscape
Evolutionary Programming Using a Mixed Strategy Adapting to Local Fitness Landscape Liang Shen Department of Computer Science Aberystwyth University Ceredigion, SY23 3DB UK lls08@aber.ac.uk Jun He Department
More informationResearch Article Multiswarm Particle Swarm Optimization with Transfer of the Best Particle
Computational Intelligence and Neuroscience Volume 2015, Article I 904713, 9 pages http://dx.doi.org/10.1155/2015/904713 Research Article Multiswarm Particle Swarm Optimization with Transfer of the Best
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 informationAvailable online at AASRI Procedia 1 (2012 ) AASRI Conference on Computational Intelligence and Bioinformatics
Available online at www.sciencedirect.com AASRI Procedia ( ) 377 383 AASRI Procedia www.elsevier.com/locate/procedia AASRI Conference on Computational Intelligence and Bioinformatics Chaotic Time Series
More informationHybrid particle swarm algorithm for solving nonlinear constraint. optimization problem [5].
Hybrid particle swarm algorithm for solving nonlinear constraint optimization problems BINGQIN QIAO, XIAOMING CHANG Computers and Software College Taiyuan University of Technology Department of Economic
More informationResearch Article Hopf Bifurcation Analysis and Anticontrol of Hopf Circles of the Rössler-Like System
Abstract and Applied Analysis Volume, Article ID 3487, 6 pages doi:.55//3487 Research Article Hopf Bifurcation Analysis and Anticontrol of Hopf Circles of the Rössler-Like System Ranchao Wu and Xiang Li
More informationNew communication schemes based on adaptive synchronization
CHAOS 17, 0114 2007 New communication schemes based on adaptive synchronization Wenwu Yu a Department of Mathematics, Southeast University, Nanjing 210096, China, Department of Electrical Engineering,
More informationEgocentric Particle Swarm Optimization
Egocentric Particle Swarm Optimization Foundations of Evolutionary Computation Mandatory Project 1 Magnus Erik Hvass Pedersen (971055) February 2005, Daimi, University of Aarhus 1 Introduction The purpose
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 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 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 informationSolving the Constrained Nonlinear Optimization based on Imperialist Competitive Algorithm. 1 Introduction
ISSN 1749-3889 (print), 1749-3897 (online) International Journal of Nonlinear Science Vol.15(2013) No.3,pp.212-219 Solving the Constrained Nonlinear Optimization based on Imperialist Competitive Algorithm
More informationA new pseudorandom number generator based on complex number chaotic equation
A new pseudorandom number generator based on complex number chaotic equation Liu Yang( 刘杨 ) and Tong Xiao-Jun( 佟晓筠 ) School of Computer Science and Technology, Harbin Institute of Technology, Weihai 264209,
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 informationArtificial Bee Colony Algorithm-based Parameter Estimation of Fractional-order Chaotic System with Time Delay
IEEE/CAA JOURNAL OF AUTOMATICA SINICA, VOL. 4, NO. 1, JANUARY 2017 107 Artificial Bee Colony Algorithm-based Parameter Estimation of Fractional-order Chaotic System with Time Delay Wenjuan Gu, Yongguang
More informationMultiple-mode switched observer-based unknown input estimation for a class of switched systems
Multiple-mode switched observer-based unknown input estimation for a class of switched systems Yantao Chen 1, Junqi Yang 1 *, Donglei Xie 1, Wei Zhang 2 1. College of Electrical Engineering and Automation,
More informationImproved Shuffled Frog Leaping Algorithm Based on Quantum Rotation Gates Guo WU 1, Li-guo FANG 1, Jian-jun LI 2 and Fan-shuo MENG 1
17 International Conference on Computer, Electronics and Communication Engineering (CECE 17 ISBN: 978-1-6595-476-9 Improved Shuffled Frog Leaping Algorithm Based on Quantum Rotation Gates Guo WU 1, Li-guo
More informationPhase Synchronization of Coupled Rossler Oscillators: Amplitude Effect
Commun. Theor. Phys. (Beijing, China) 47 (2007) pp. 265 269 c International Academic Publishers Vol. 47, No. 2, February 15, 2007 Phase Synchronization of Coupled Rossler Oscillators: Amplitude Effect
More informationGaussian Harmony Search Algorithm: A Novel Method for Loney s Solenoid Problem
IEEE TRANSACTIONS ON MAGNETICS, VOL. 50, NO., MARCH 2014 7026405 Gaussian Harmony Search Algorithm: A Novel Method for Loney s Solenoid Problem Haibin Duan and Junnan Li State Key Laboratory of Virtual
More informationSecure Communication Using H Chaotic Synchronization and International Data Encryption Algorithm
Secure Communication Using H Chaotic Synchronization and International Data Encryption Algorithm Gwo-Ruey Yu Department of Electrical Engineering I-Shou University aohsiung County 840, Taiwan gwoyu@isu.edu.tw
More informationA Method of HVAC Process Object Identification Based on PSO
2017 3 45 313 doi 10.3969 j.issn.1673-7237.2017.03.004 a a b a. b. 201804 PID PID 2 TU831 A 1673-7237 2017 03-0019-05 A Method of HVAC Process Object Identification Based on PSO HOU Dan - lin a PAN Yi
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 informationResearch Article Data-Driven Fault Diagnosis Method for Power Transformers Using Modified Kriging Model
Hindawi Mathematical Problems in Engineering Volume 2017, Article ID 3068548, 5 pages https://doi.org/10.1155/2017/3068548 Research Article Data-Driven Fault Diagnosis Method for Power Transformers Using
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 informationThe particle swarm optimization algorithm: convergence analysis and parameter selection
Information Processing Letters 85 (2003) 317 325 www.elsevier.com/locate/ipl The particle swarm optimization algorithm: convergence analysis and parameter selection Ioan Cristian Trelea INA P-G, UMR Génie
More informationConsolidation properties of dredger fill under surcharge preloading in coast region of Tianjin
30 2 2011 6 GLOBAL GEOLOGY Vol. 30 No. 2 Jun. 2011 1004-5589 2011 02-0289 - 07 1 1 2 3 4 4 1. 130026 2. 130026 3. 110015 4. 430074 45 cm 100% ` TU447 A doi 10. 3969 /j. issn. 1004-5589. 2011. 02. 020 Consolidation
More informationAN EFFICIENT CHARGED SYSTEM SEARCH USING CHAOS FOR GLOBAL OPTIMIZATION PROBLEMS
INTERNATIONAL JOURNAL OF OPTIMIZATION IN CIVIL ENGINEERING Int. J.Optim. Civil Eng. 2011; 2:305-325 AN EFFICIENT CHARGED SYSTEM SEARCH USING CHAOS FOR GLOBAL OPTIMIZATION PROBLEMS S. Talatahari 1, A. Kaveh
More informationA Scalability Test for Accelerated DE Using Generalized Opposition-Based Learning
009 Ninth International Conference on Intelligent Systems Design and Applications A Scalability Test for Accelerated DE Using Generalized Opposition-Based Learning Hui Wang, Zhijian Wu, Shahryar Rahnamayan,
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 informationExperimental and numerical simulation studies of the squeezing dynamics of the UBVT system with a hole-plug device
Experimental numerical simulation studies of the squeezing dynamics of the UBVT system with a hole-plug device Wen-bin Gu 1 Yun-hao Hu 2 Zhen-xiong Wang 3 Jian-qing Liu 4 Xiao-hua Yu 5 Jiang-hai Chen 6
More informationFinite Time Synchronization between Two Different Chaotic Systems with Uncertain Parameters
www.ccsenet.org/cis Coputer and Inforation Science Vol., No. ; August 00 Finite Tie Synchronization between Two Different Chaotic Systes with Uncertain Paraeters Abstract Wanli Yang, Xiaodong Xia, Yucai
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 informationAnti-synchronization Between Coupled Networks with Two Active Forms
Commun. Theor. Phys. 55 (211) 835 84 Vol. 55, No. 5, May 15, 211 Anti-synchronization Between Coupled Networks with Two Active Forms WU Yong-Qing ( ï), 1 SUN Wei-Gang (êå ), 2, and LI Shan-Shan (Ó ) 3
More informationInvestigation of Mutation Strategies in Differential Evolution for Solving Global Optimization Problems
Investigation of Mutation Strategies in Differential Evolution for Solving Global Optimization Problems Miguel Leon Ortiz and Ning Xiong Mälardalen University, Västerås, SWEDEN Abstract. Differential evolution
More informationAdaptive Differential Evolution and Exponential Crossover
Proceedings of the International Multiconference on Computer Science and Information Technology pp. 927 931 ISBN 978-83-60810-14-9 ISSN 1896-7094 Adaptive Differential Evolution and Exponential Crossover
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 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 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 informationToward Effective Initialization for Large-Scale Search Spaces
Toward Effective Initialization for Large-Scale Search Spaces Shahryar Rahnamayan University of Ontario Institute of Technology (UOIT) Faculty of Engineering and Applied Science 000 Simcoe Street North
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 informationAn Improved F-Expansion Method and Its Application to Coupled Drinfel d Sokolov Wilson Equation
Commun. Theor. Phys. (Beijing, China) 50 (008) pp. 309 314 c Chinese Physical Society Vol. 50, No., August 15, 008 An Improved F-Expansion Method and Its Application to Coupled Drinfel d Sokolov Wilson
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 informationarxiv: v1 [cs.ne] 29 Jul 2014
A CUDA-Based Real Parameter Optimization Benchmark Ke Ding and Ying Tan School of Electronics Engineering and Computer Science, Peking University arxiv:1407.7737v1 [cs.ne] 29 Jul 2014 Abstract. Benchmarking
More informationEffects of Atomic Coherence and Injected Classical Field on Chaotic Dynamics of Non-degenerate Cascade Two-Photon Lasers
Commun. Theor. Phys. Beijing China) 48 2007) pp. 288 294 c International Academic Publishers Vol. 48 No. 2 August 15 2007 Effects of Atomic Coherence and Injected Classical Field on Chaotic Dynamics of
More informationReliability-Based Microstructural Topology Design with Respect to Vibro-Acoustic Criteria
11 th World Congress on Structural and Multidisciplinary Optimisation 07 th -12 th, June 2015, Sydney Australia Reliability-Based Microstructural Topology Design with Respect to Vibro-Acoustic Criteria
More informationDynamics of slow and fast systems on complex networks
Indian Academy of Sciences Conference Series (2017) 1:1 DOI: 10.29195/iascs.01.01.0003 Indian Academy of Sciences Dynamics of slow and fast systems on complex networks KAJARI GUPTA and G. AMBIKA * Indian
More informationQuantum-Inspired Differential Evolution with Particle Swarm Optimization for Knapsack Problem
JOURNAL OF INFORMATION SCIENCE AND ENGINEERING 31, 1757-1773 (2015) Quantum-Inspired Differential Evolution with Particle Swarm Optimization for Knapsack Problem DJAAFAR ZOUACHE 1 AND ABDELOUAHAB MOUSSAOUI
More informationAn Improved Quantum Evolutionary Algorithm with 2-Crossovers
An Improved Quantum Evolutionary Algorithm with 2-Crossovers Zhihui Xing 1, Haibin Duan 1,2, and Chunfang Xu 1 1 School of Automation Science and Electrical Engineering, Beihang University, Beijing, 100191,
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 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 informationResearch Article Adaptive Control of Chaos in Chua s Circuit
Mathematical Problems in Engineering Volume 2011, Article ID 620946, 14 pages doi:10.1155/2011/620946 Research Article Adaptive Control of Chaos in Chua s Circuit Weiping Guo and Diantong Liu Institute
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 informationResearch Article On the Stability Property of the Infection-Free Equilibrium of a Viral Infection Model
Hindawi Publishing Corporation Discrete Dynamics in Nature and Society Volume, Article ID 644, 9 pages doi:.55//644 Research Article On the Stability Property of the Infection-Free Equilibrium of a Viral
More informationNew Integrable Decomposition of Super AKNS Equation
Commun. Theor. Phys. (Beijing, China) 54 (2010) pp. 803 808 c Chinese Physical Society and IOP Publishing Ltd Vol. 54, No. 5, November 15, 2010 New Integrable Decomposition of Super AKNS Equation JI Jie
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 informationCenter-based initialization for large-scale blackbox
See discussions, stats, and author profiles for this publication at: http://www.researchgate.net/publication/903587 Center-based initialization for large-scale blackbox problems ARTICLE FEBRUARY 009 READS
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 informationSynchronization of a General Delayed Complex Dynamical Network via Adaptive Feedback
Synchronization of a General Delayed Complex Dynamical Network via Adaptive Feedback Qunjiao Zhang and Junan Lu College of Mathematics and Statistics State Key Laboratory of Software Engineering Wuhan
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 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 information