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Hopf Bifurcation of Compound Stochastic van der Pol System

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  • Shaojuan Ma
  • Qianling Zhang

Abstract

Hopf bifurcation analysis for compound stochastic van der Pol system with a bound random parameter and Gaussian white noise is investigated in this paper. By the Karhunen-Loeve (K-L) expansion and the orthogonal polynomial approximation, the equivalent deterministic van der Pol system can be deduced. Based on the bifurcation theory of nonlinear deterministic system, the critical value of bifurcation parameter is obtained and the influence of random strength and noise intensity on stochastic Hopf bifurcation in compound stochastic system is discussed. At last we found that increased can relocate the critical value of bifurcation parameter forward while increased makes it backward and the influence of is more sensitive than . The results are verified by numerical simulations.

Suggested Citation

  • Shaojuan Ma & Qianling Zhang, 2016. "Hopf Bifurcation of Compound Stochastic van der Pol System," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-7, June.
    • Handle: RePEc:hin:jnlmpe:4246916
    DOI: 10.1155/2016/4246916
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