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Hopf Bifurcations of a Stochastic Fractional‐Order Van der Pol System

Author

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  • Xiaojun Liu
  • Ling Hong
  • Lixin Yang

Abstract

The Hopf bifurcation of a fractional‐order Van der Pol (VDP for short) system with a random parameter is investigated. Firstly, the Chebyshev polynomial approximation is applied to study the stochastic fractional‐order system. Based on the method, the stochastic system is reduced to the equivalent deterministic one, and then the responses of the stochastic system can be obtained by numerical methods. Then, according to the existence conditions of Hopf bifurcation, the critical parameter value of the bifurcation is obtained by theoretical analysis. Then, numerical simulations are carried out to verify the theoretical results.

Suggested Citation

  • Xiaojun Liu & Ling Hong & Lixin Yang, 2014. "Hopf Bifurcations of a Stochastic Fractional‐Order Van der Pol System," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:835482
    DOI: 10.1155/2014/835482
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    References listed on IDEAS

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    1. Chen, Juhn-Horng & Chen, Wei-Ching, 2008. "Chaotic dynamics of the fractionally damped van der Pol equation," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 188-198.
    2. Ge, Zheng-Ming & Ou, Chan-Yi, 2007. "Chaos in a fractional order modified Duffing system," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 262-291.
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