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Chaos control and synchronization of the Φ6-Van der Pol system driven by external and parametric excitations

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Abstract

The dynamical behavior of the Φ6-Van der Pol system subjected to both external and parametric excitation is investigated. The effect of parametric excitation amplitude on the routes to chaos is studied by numerical analysis. It is found that the probability of chaos happening increases along with the parametric excitation amplitude increases while the external excitation amplitude fixed. Based on the invariance principle of differential equations, the system is lead to desirable periodic orbit or chaotic state (synchronization) with different control techniques. Numerical simulations are provided to validate the proposed method.

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Authors and Affiliations

  1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, 710072, China

    Li Ruihong, Xu Wei & Li Shuang

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  1. Li Ruihong
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  2. Xu Wei
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  3. Li Shuang
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Correspondence to Li Ruihong.

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Ruihong, L., Wei, X. & Shuang, L. Chaos control and synchronization of the Φ6-Van der Pol system driven by external and parametric excitations. Nonlinear Dyn 53, 261–271 (2008). https://doi.org/10.1007/s11071-007-9313-3

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  • DOI: https://doi.org/10.1007/s11071-007-9313-3

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