Before revision:  By adapting a method based on  the discrete-time Markov process , we provide here a general analytic tool for the reaction dynamics of systems with a small number of molecules.
After revision:  By adapting a method based on a Markov process with a tridiagonal transition matrix is applied to the analysis of this transition in reaction dynamics. The transition to bistability due to the discrete-time Markov process , we provide here a general analytic tool for the reaction dynamics of systems with a small number of molecules.