Kinetics of a Verhulst-type system with nonlinearly coupled noise

摘要

The stochastic Bernoulli equation with nonlinearly coupled dichotomous noise is exactly solved by direct averaging. The similar system driven by the periodic perturbation with a random phase is also considered. The results concerning the kinetic and stationary properties in both cases are compared. The evolution of the mean value from the initial states located close to the equilibrium state is found to be nonmonotonic.