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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; b The Aeronautical Science Key Laboratory for Smart Material and Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 2100 |
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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.
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Received: 26 February 2011
Revised: 25 April 2011
Accepted manuscript online:
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PACS:
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05.45.-a
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(Nonlinear dynamics and chaos)
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Fund: Project supported by the National Natural Science Foundation of China (Grant No. 60973097). |
Cite this article:
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 2011 Chin. Phys. B 20 080503
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