Stochastic Analysis of a Nonlinear Model System

梁鍹廣(H. K. Leung)

Chinese Journal of Physics

26卷3期（1988 / 08 / 01）

159 - 170

英文

We investigate a special model system in which the two stable steady states are separated by one unstable absorbing steady state. The stochastic properties of the model system are studied by considering the internal and external fluctuations. We employ both Stratonovich and Ito interpretations of stochastic calculus to treat the external white-noises which include additive noises and multiplicative noises of various types. For each noise, it is found that the stable steady states will turn out to be unstable as the noise parameter approaches a specific value, and that the transient properties of the system will becomes complicated. As in the quadratic nonlinear system, the cubic system exhibits critical slowing-down near the instability point induced by mixedorder multiplicative noise. The critical exponent characterizing this unique process is found numerically to be equal to the mean field value well-known in the equilibrium phase transition.