Hopf bifurcation of the stochastic model on business cycle

A stochastic model on business cycle was presented in thas paper. Simplifying the model through the quasi Hamiltonian theory, the Ito diffusion process Was obtained. According to Oseledec multiplicative ergodic theory and singular boundary theory, the conditions of local and global stability were acquired. Solving the stationary FPK equation and analyzing the stationary probability density, the stochastic Hopf bifurcation was explained. The result indicated that the change of parameter a was the key factor to the appearance of the stochastic Hopf bifurcation.