ON THE HOPF BIFURCATION SYSTEM IN THE PRESENCE OF PARAMETRIC REAL NOISES

With the aid of the stochastic averaging method,the theory of singular points of diffusion processes and the method of invariant measure, a Hopf bifurcation system in the presence of parametric real noises is studied. It is found that in this nonlinear stochastic system, due tothe presence of the parametric real noises, a change of the type of bifurcation takes place and two bifurcation points appear, which differ from the original Hopf bifurcation one.