STOCHASTIC HOPF BIFURCATIONS

A nonlinear model system of chemical reaction, which exhibits supercri tical Hopf bifurcation is studied stochastically by taking white noise into consideration. Both the asymptotic properties near the bifurcati on point and the transient processes preceding to the competing attrac tors are emphasized. It is found that both additive and multiplicative noises tend to suppress periodicity, and that only the additive noise s could induce transition from a limit cycle to a fixed point. This fi nding is in accord with the previous results that Hopf bifurcation is always postponed by noises. Extensive investigation results in a phase diagram showing the phase domains of competing attractors. The phase boundaries are interpreted as the bifurcation loci for the stochastic Hopf bifurcation.