Capture of stochastic P-bifurcation in a delayed mechanical centrifugal governor

Abstract

This paper proposes a stochastic delay model for a mechanical centrifugal governor system with noise. The Hopf bifurcation of the system is obtained with the delay as a parameter. Considering the effect of delay, the stochastic bifurcation of the system is obtained, as well as the stochastic bifurcation diagrams of the model by numerical analysis. It is found that large delays can lead to the occurrence of stochastic bifurcations, which destabilize the system. Moreover, retaining the quadratic term of ϵ induces a new dynamical phenomenon - stochastic P-bifurcation. When spectral density is used as a bifurcation parameter, the periodicity of the system is influenced. The results of this paper are a reference value for preventing instability in mechanical systems. Meanwhile, the theoretical work and numerical simulations in this paper can be extended to other systems.