Research on Stochastic Hopf Bifurcation of Elastic Constraint Wheelset System

Considering random track irregularities and their random structure parameters,the Ito stochastic differential equation set was established for the elastic wheel system.According to the stochastic averaging method,the Ito stochastic differential equation set was expressed as the one-dimensional diffusion process.The maximal Lyapunov exponent was calculated by the quasi non-integrable hamiltonian theory and oseledec multiplicative ergodic theory,and the local stochastic stability conditions were obtained.The stochastic global stability conditions were also obtained by judging the modality of the singular boundary.The stochastic Hopf bifurcation types were analyzed from the steady-state probability density and joint probability density,and the conditions of stochastic Hopf bifurcation were discussed.The results show as follows:Different random strength effects on the wheelset system have different critical instability speeds,even if certain bifurcation conditions are satisfied,bifurcation does not have to occur;the possibility of occurrence of bifurcation is evaluated by the probability calculated.