Generalized Synchronization of Stochastic Discrete Chaotic System with Poisson Distribution Coefficient

Shao-Juan Ma,Jie Zheng,Duan Dong

doi:10.1155/2013/981503

Shao-Juan Ma, Jie Zheng + Show 1 more

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https://doi.org/10.1155/2013/981503

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Abstract

This paper addresses the generalized synchronization of stochastic discrete chaotic systems with Poisson distribution coefficient. Firstly, based on the orthogonal polynomial approximation theory of discrete random function in Hilbert spaces, the discrete chaotic system with random parameter is transformed into its equivalent deterministic system. Secondly, a general method for the generalized synchronization of discrete chaotic system with random parameter is presented by Lyapunov stability theory and contraction theorem. Finally, two synchronization examples numerically illustrated that the proposed control scheme is effective for any stochastic discrete system.

Highlights

Synchronization is a kind of typical collective behavior and basic motion in nature
This paper addresses the generalized synchronization of stochastic discrete chaotic systems with Poisson distribution coefficient
Many different types of synchronization methods such as phase synchronization [3], partial synchronization [4], projective synchronization [5, 6], lag synchronization [7], complete synchronization [8], Q-S synchronization [9], fast synchronization [10], and adaptive impulsive synchronization [11] have been presented in continuous-time chaotic systems in the past two decades

Summary

Introduction

Synchronization is a kind of typical collective behavior and basic motion in nature. Since Pecora and Carroll [1] showed that it is possible to synchronize the coupled chaotic dynamical system with different initial conditions, chaos synchronization has been extensively studied due to its theoretical challenge and great potential application in secure communication, neuroscience, encoding message, chemical reaction, and complex networks [2]. Based on statistical characteristics of the Poisson distribution and the orthogonal polynomial approximation of discrete random function, substituting (6) and (7) into (4) and multiplying Pj(k) (j = 0, 1) in both sides, by taking expectation with respect to k, we get its approximate equivalent deterministic system of Lorenz discrete system with random parameter as x0 (n+1) = (1+αβ) x0 (n).

Generalized Synchronization for the Discrete Systems with Random Parameter

Illustrative Examples

Conclusions