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Taming Chaotic Arrays By Parametric Excitation With Proper Random Phase

Author

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  • KAI LEUNG YUNG

    (Department of Industrial and Systems Engineering, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China)

  • YOUMING LEI

    (Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China)

  • YAN XU

    (Department of Industrial and Systems Engineering, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China)

Abstract

A weak harmonic parametric excitation with random phase has been introduced to tame chaotic arrays. It has been shown that when the amplitude of random phase properly increases, two different kinds of chaotic arrays, unsynchronized and synchronized, can be controlled by the criterion of top Lyapunov exponent. The Lyapunov exponent was computed based on Khasminskii's formulation and the extension of Wedig's algorithm for linear stochastic systems. In particular, it was found that with stronger coupling the synchronized chaotic arrays are more controllable than the unsynchronized ones. The bifurcation analysis, the spatiotemporal evolution, and the Poincaré map were carried out to confirm the results of the top Lyapunov exponent on the dynamical behavior of control stability. Excellent agreement was found between these results.

Suggested Citation

  • Kai Leung Yung & Youming Lei & Yan Xu, 2009. "Taming Chaotic Arrays By Parametric Excitation With Proper Random Phase," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 20(10), pages 1633-1643.
    • Handle: RePEc:wsi:ijmpcx:v:20:y:2009:i:10:n:s0129183109014643
    DOI: 10.1142/S0129183109014643
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