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

doi:10.1088/1674-1056/20/8/080503

中国物理B ›› 2011, Vol. 20 ›› Issue (8): 80503-080503.doi: 10.1088/1674-1056/20/8/080503

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

张俊峰¹, 裴秋雨¹, 张晓丽²

(1)Department of Computer Science and Engineering, Henan University of Urban Construction, Pingdingshan 467036, China; (2)Department of Computer Science and Engineering, Henan University of Urban Construction, Pingdingshan 467036, China; The Aeronautical Science Key Laboratory for Smart Material and Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 2100

收稿日期:2011-02-26 修回日期:2011-04-25 出版日期:2011-08-15 发布日期:2011-08-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 60973097).

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

Zhang Jun-Feng(张俊峰)^a)†, Pei Qiu-Yu(裴秋雨)^a), and Zhang Xiao-Li(张晓丽)^a)b)

^a Department of Computer Science and Engineering, Henan University of Urban Construction, Pingdingshan 467036, China; ^bThe Aeronautical Science Key Laboratory for Smart Material and Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 2100

Received:2011-02-26 Revised:2011-04-25 Online:2011-08-15 Published:2011-08-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 60973097).

摘要/Abstract

摘要： 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.

关键词: fractional-order unified chaotic system, hybrid synchronization, linear controller, single drive variable

Abstract: 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.

Key words: fractional-order unified chaotic system, hybrid synchronization, linear controller, single drive variable

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

张俊峰, 裴秋雨, 张晓丽. A new kind of nonlinear phenomenon in coupled fractional-order chaotic systems: coexistence of anti-phase and complete synchronization[J]. 中国物理B, 2011, 20(8): 80503-080503.

Zhang Jun-Feng(张俊峰), Pei Qiu-Yu(裴秋雨), and Zhang Xiao-Li(张晓丽) . A new kind of nonlinear phenomenon in coupled fractional-order chaotic systems: coexistence of anti-phase and complete synchronization[J]. Chin. Phys. B, 2011, 20(8): 80503-080503.

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

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

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