The invariant measure and stationary probability density computing model based analysis of the governor system

Abstract

In this paper, the stochastic stability and bifurcation of a stochastic differential equation modeling a hexagonal governor system are investigated. More precisely, we introduced the stochasticity into the model based on the parameter perturbation, and simplified the stochastic hexagonal governor system by using the stochastic center manifold theory and stochastic average theory. Besides, we investigated the local stochastic stability and global stochastic stability of the stochastic hexagonal governor system through the use of the Lyapunov exponent and singular boundary theory. And based on the invariant measure and stationary probability density, we studied the stochastic bifurcation of the stochastic hexagonal governor system. Finally, we obtained some new criteria to ensure the stochastic pitchfork bifurcation and P-bifurcation of the stochastic hexagonal governor system.