Dynamic Behaviors Of The Stochastic CSTR And Enzymatic Reaction Model

The chemical reaction dynamics mainly studies the process of chemical reactions and the change of reactant concentration over time,using mathematical models to study chemical reaction systems.Its object of study is a dynamic system whose properties change over time.The dynamical behaviors of stochastic chemical reaction models has a wider application background.In the real world,the impact of ambient white noise on models of chemical reactions is inevitable.Therefore,this paper mainly studies the dynamic behavior of the continuous stirred tank reactor(CSTR)and enzymatic reaction model under random disturbance,as follows:1.Study on random continuous stirred tank reactor(CSTR)system.A stochastic CSTR model with perturbation of reaction rate coefficient is considered in this paper.Firstly,the existence and uniqueness of the positive solution of the stochastic chemical reaction is proved.Then we show that the stochastic reaction system has ergodicity and a stationary distribution.At last,we make some simulations to illustrate above theoretical results.The most interesting result is: the stationary-state of the determined continuous stirred tank reactor model may be have nine structures of different property,but no matter what dynamic behavior the deterministic model presents,the corresponding stochastic model always has a stationary distribution,without any additional conditions.2.Study on stochastic negative feedback enzymatic reaction system.In this paper,a negative feedback enzymatic reaction model with white noise disturbance is constructed and analyzed.Firstly,it is proved that the solution of the stochastic enzymatic reaction system is positive and global.Then,by constructing an appropriate Lyapunov function,it is proved that the stochastic enzymatic reaction system has a stationary distribution,and the corresponding random model is always ergodic without any additional conditions.