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Global dynamics of two coupled parametrically excited van der Pol oscillators

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  • Wang, Xia
  • Chen, Fangqi

Abstract

Using a combination of analytical and numerical methods, the global bifurcations and chaotic dynamics of two non-linearly coupled parametrically excited van der Pol oscillators are investigated in detail. With the aid of the method of multiple scales, the slow flow equations are obtained. Based on the slow flow equations, normal form theory and the techniques of choosing complementary space are applied to find the explicit expressions of the simpler normal form associated with a double zero and a pair of pure imaginary eigenvalues. By the simpler normal form, using the global perturbation method developed by Kovacic and Wiggins, the analysis of global bifurcation and chaotic dynamics of two non-linearly coupled parametrically excited van der Pol oscillators is given. The results indicate that there exists a Silnikov type single-pulse homoclinic orbit for this class of system which implies the chaotic motions can occur. Numerical simulations are also given and verify the analytical predictions.

Suggested Citation

  • Wang, Xia & Chen, Fangqi, 2012. "Global dynamics of two coupled parametrically excited van der Pol oscillators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(9), pages 1551-1571.
    • Handle: RePEc:eee:matcom:v:82:y:2012:i:9:p:1551-1571
    DOI: 10.1016/j.matcom.2012.02.006
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    References listed on IDEAS

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    1. Zhang, W. & Zu, J.W. & Wang, F.X., 2008. "Global bifurcations and chaos for a rotor-active magnetic bearing system with time-varying stiffness," Chaos, Solitons & Fractals, Elsevier, vol. 35(3), pages 586-608.
    2. Cao, D.X. & Zhang, W., 2008. "Global bifurcations and chaotic dynamics for a string-beam coupled system," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 858-875.
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