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Nonlinear Dynamics

, Volume 53, Issue 3, pp 261–271 | Cite as

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

  • Li Ruihong
  • Xu Wei
  • Li Shuang
Original Paper

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.

Keywords

Φ6-Van der Pol system Parametric excitation Bifurcation Largest Lyapunov exponent Chaos control Synchronization Invariance principle of differential equations 

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Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Department of Applied MathematicsNorthwestern Polytechnical UniversityXi’anChina

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