Hopf bifurcation in a kind of stochastic van der Pol system

Abstract

The Hopf bifurcation of van der Pol system with random parameter is studied. Firstly according to the orthogonal polynomial approximation in Hilbert space, the van der Pol system with random parameter can be reduced into the equivalent deterministic system. Then the Hopf bifurcation can be explored by the traditional methods in deterministic bifurcation theory. After the critical point of Hopf bifurcation in stochastic van der Pol system is obtained, the influence of the random parameter on Hopf bifurcation in stochastic van der Pol system is analyzed. At last we verified these results by numerical simulations.