Critical phenomenon of a two component nonlinear stochastic system

In this paper, we introduce a nonlinear stochastic model with two components. Interaction is allowed between the two components of the system. A detailed discussion is given of the relation of the interaction to the stationary distributions of the system. Let α be the transition rate from the first component to the second. It is shown, by concrete examples, that the number of stationary distributions varies as α crosses some critical values. These results provide a qualitatively correct picture for some phenomena in physics and chemistry.