A new kind of nonlinear fractional-order chaotic phenomenon in coupled systems： coexistence of anti-phase and complete synchronization

In this paper, we have found a kind of interesting nonlinear phenomenon hybrid synchronization in linearly coupled fractional-order chaotic systems. This new synchronization mechanism, i.e., part of state variables are anti- phase synchronized and part completely synchronized, can be achieved using...

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Published in中国物理：英文版 Vol. 20; no. 8; pp. 90 - 96
Main Author Zhang Jun-Feng Pei Qiu-Yu Zhang Xiao-Li
Format Journal Article
LanguageEnglish
Published 2011
Subjects
共存
分数阶系统
反相位
同步机制
完全同步
混沌现象
线性控制器
非线性耦合系统
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Summary:In this paper, we have found a kind of interesting nonlinear phenomenon hybrid synchronization in linearly coupled fractional-order chaotic systems. This new synchronization mechanism, i.e., part of state variables are anti- phase synchronized and part completely synchronized, can be achieved using a single linear controller with only one drive variable. Based on the stability theory of the fractional-order system, we investigated the possible existence of this new synchronization mechanism. Moreover, a helpful theorem, serving as a determinant for the gain of the controller, is also presented. Solutions of coupled systems are obtained numerically by an improved Adams Bashforth-Moulton algorithm. To support our theoretical analysis, simulation results are given.
Bibliography:In this paper, we have found a kind of interesting nonlinear phenomenon hybrid synchronization in linearly coupled fractional-order chaotic systems. This new synchronization mechanism, i.e., part of state variables are anti- phase synchronized and part completely synchronized, can be achieved using a single linear controller with only one drive variable. Based on the stability theory of the fractional-order system, we investigated the possible existence of this new synchronization mechanism. Moreover, a helpful theorem, serving as a determinant for the gain of the controller, is also presented. Solutions of coupled systems are obtained numerically by an improved Adams Bashforth-Moulton algorithm. To support our theoretical analysis, simulation results are given.
fractional-order unified chaotic system, hybrid synchronization, linear controller, singledrive variable
11-5639/O4
ISSN:1674-1056
2058-3834