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Adaptive synchronization of two chaotic systems with stochastic unknown parameters

Salarieh, H ; Sharif University of Technology | 2009

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  1. Type of Document: Article
  2. DOI: 10.1016/j.cnsns.2007.09.002
  3. Publisher: 2009
  4. Abstract:
  5. Using the Lyapunov stability theory an adaptive control is proposed for chaos synchronization between two different systems which have stochastically time varying unknown coefficients. The stochastic variations of the coefficients about their unknown mean values are modeled through white Gaussian noise produced by the Weiner process. It is shown that using the proposed adaptive control the mean square of synchronization error converges to an arbitrarily small bound around zero. To demonstrate the effectiveness of the proposed technique, it is applied to the Lorenz-Chen and the Chen-Rossler dynamical systems, as some case studies. Simulation results indicate that the proposed adaptive controller has a high performance in synchronization of chaotic systems in noisy environment. © 2007 Elsevier B.V. All rights reserved
  6. Keywords:
  7. Lyapunov stability ; Stochastic chaos ; Adaptive control systems ; Adaptive systems ; Chaos theory ; Control systems ; Control theory ; Dynamical systems ; Military data processing ; Schrodinger equation ; Stability ; Stochastic programming ; Synchronization ; Adaptive Control ; Adaptive controllers ; Adaptive synchronizations ; Case studies ; Chaos synchronization (CS) ; Lyapunov stability theory ; Mean square (MS) ; Mean value (MV) ; Noisy environments ; Rossler ; Simulation results ; Stochastic variations ; Synchronization errors ; Time varying ; Unknown coefficients ; Unknown parameters ; Weiner process ; White Gaussian noise (WGN) ; Chaotic systems
  8. Source: Communications in Nonlinear Science and Numerical Simulation ; Volume 14, Issue 2 , 2009 , Pages 508-519 ; 10075704 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/pii/S1007570407002419