Dynamics of the Noise-Induced Phase Transition of the Verhulst Model

Abstract

Langevin-type equation with a nonlinear drift term and a multiplicative noise term is treated. Dynamical aspects of noise-induced phase transition are studied with the aid of the method of asymptotic iteration (MAl) introduced in a previous paper. The temporal behavior of the first moment is solved exactly. It is shown that the critical slowing down does not occur at the so-called transition point.