Attaining chaos synchronization by using the non-generating partitions

Abstract In this study, we show that, the unidirectional chaos synchronization can be obtained by using a non-generating partition to divide the phase space. Moreover, when using a non-generating partition to attain the chaos synchronization, the minimum required communication channel capacity is h β , which is less than the KS entropy of the drive system h K S . However, the minimum synchronization error cannot be arbitrarily small. Simulations are provided to validate our results.

[1]  Shawn D. Pethel,et al.  Experimental targeting of chaos via controlled symbolic dynamics , 2003 .

[2]  Louis M. Pecora,et al.  Synchronizing chaotic circuits , 1991 .

[3]  Yan-Jun Liu,et al.  Adaptive fuzzy control for a class of uncertain nonaffine nonlinear systems , 2007, Inf. Sci..

[4]  Shaocheng Tong,et al.  Adaptive Neural Output Feedback Tracking Control for a Class of Uncertain Discrete-Time Nonlinear Systems , 2011, IEEE Transactions on Neural Networks.

[5]  Zhao Yan,et al.  A unified approach to fuzzy modelling and robust synchronization of different hyperchaotic systems , 2008 .

[6]  Zhang Huaguang,et al.  Modeling, identification, and control of a class of nonlinear systems , 2001, IEEE Trans. Fuzzy Syst..

[7]  Fu Jie,et al.  A practical approach to robust impulsive lag synchronization between different chaotic systems , 2008 .

[8]  R. Devaney.  An Introduction to Chaotic Dynamical Systems , 1990 .

[9]  Ned J Corron,et al.  Information flow in chaos synchronization: fundamental tradeoffs in precision, delay, and anticipation. , 2003, Physical review letters.

[10]  M. Hénon,et al.  A two-dimensional mapping with a strange attractor , 1976 .

[11]  Yanjun Liu,et al.  Adaptive robust fuzzy control for a class of uncertain chaotic systems , 2009 .

[12]  Xingyuan Wang,et al.  The least channel capacity for chaos synchronization. , 2011, Chaos.

[13]  Lai,et al.  Estimating generating partitions of chaotic systems by unstable periodic orbits , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[14]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[15]  Erik M. Bollt,et al.  Encoding information in chemical chaos by controlling symbolic dynamics , 1997 .

[16]  Xingyuan Wang,et al.  Chaos synchronization basing on symbolic dynamics with nongenerating partition. , 2009, Chaos.

[17]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[18]  Ned J Corron,et al.  Synchronizing the information content of a chaotic map and flow via symbolic dynamics. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  Huaguang Zhang,et al.  Adaptive Synchronization Between Two Different Chaotic Neural Networks With Time Delay , 2007, IEEE Transactions on Neural Networks.

[20]  Ljupco Kocarev,et al.  Applications of symbolic dynamics in chaos synchronization , 1997 .

[21]  Shaocheng Tong,et al.  Adaptive Neural Output Feedback Controller Design With Reduced-Order Observer for a Class of Uncertain Nonlinear SISO Systems , 2011, IEEE Transactions on Neural Networks.

[22]  Shaocheng Tong,et al.  Robust Adaptive Tracking Control for Nonlinear Systems Based on Bounds of Fuzzy Approximation Parameters , 2010, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[23]  Alexander L. Fradkov,et al.  Chaotic observer-based synchronization under information constraints. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Bai-Lin Haot,et al.  Applied Symbolic Dynamics , 1998 .