The dynamics of the stochastic multi-molecule biochemical reaction model

Abstract

The paper introduces the dynamics of a stochastic multi-molecule biochemical reaction model.First, we show that there is a unique positive solution of the stochastic model. Furthermore, we deduce the conditions when the reaction will end and when the reaction being proceed. At last, we derive that the solution of (1.5) oscillates around the endemic proportion equilibrium $$P^*(x^*,y^*)$$ , and the intensity of fluctuation is proportional to white noise. The key to the analysis in this paper is choosing appropriate Lyapunov function. The outcomes are illustrated by computer simulations throughout this paper.