Stochastic Hopf Bifurcations

H. K. Leung

Chinese Journal of Physics

35卷1期（1997 / 02 / 01）

47 - 55

英文

A nonlinear model system of chemical reaction, which exhibits supercritical Hopf bifurcation is studied stochastically by taking white noise into consideration. Both the asymptotic properties near the bifurcation point and the transient processes preceding to the competing attractors are emphasized. It is found that both additive and multiplicative noises tend to suppress periodicity, and that only the additive noises could induce transition from a limit cycle to a fixed point. This finding 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.

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