Research on stochastic stability and stochastic bifurcation of suspended wheelset

We studied the stochastic stability and bifurcation behavior for a suspended wheelset system in the presence of a Gauss white noise stochastic parametric excitation. First, the global stochastic stability was researched by judging the modality of the singular boundary. Then, the diffusion exponent, drift exponent and character value of the two boundaries were calculated. After getting the maximal Lyapunov exponent, the condition of D-bifurcation was obtained. By analyzing the shape and peaks of the stationary probability density function, the condition of stochastic P-bifurcation was also obtained. Finally, the numerical verification and the comparison between deterministic bifurcation and P-bifurcation were performed. The results show that the random excitation shifts the critical velocity to a lower value, and the stochastic system becomes more sensitive and more unstable. The stochastic parametric excitation can destroy the origin subcritical Hopf bifurcation in the deterministic system.