Dynamical behaviors of a stochastic multi-molecule biochemical reaction model with Ornstein-Uhlenbeck process

Abstract

In this paper, we develop a stochastic multi-molecule chemical reaction model with reaction rate perturbed by log-normal \(Ornstein-Uhlenbeck\) process in order to consider the effects of random factors on chemical reaction dynamics. Firstly, we prove the existence and uniqueness of the global positive solution for the stochastic model. In addition, we obtain the conditions under which the corresponding stochastic system exist a stationary distribution. Then, we derive a sufficient condition to end the reaction. Furthermore, the stochastic system has been transformed into a linearized system, by solving \(Fokker-Planck\) equation, we obtain the exact expression of the density function around the quasi-equilibrium of this system. Finally, we draw a conclusion that the dynamical behaviors of the stochastic system will be affected by random factor, \(Ornstein-Uhlenbeck\) process respectively