Hopf bifurcation of nonlinear system with multisource stochastic factors

Abstract

The article mainly explores the Hopf bifurcation of a kind of nonlinear system with Gaussian white noise excitation and bounded random parameter. Firstly, the nonlinear system with multisource stochastic factors is reduced to an equivalent deterministic nonlinear system by the sequential orthogonal decomposition method and the Karhunen–Loeve (K-L) decomposition theory. Secondly, the critical conditions about the Hopf bifurcation of the equivalent deterministic system are obtained. At the same time the influence of multisource stochastic factors on the Hopf bifurcation for the proposed system is explored. Finally, the theorical results are verified by the numerical simulations.

Keywords

• Multisource stochastic factors
• Gaussian white noise
• K-L decomposition
• Hopf bifurcation
• Random parameter