Study On Dynamic Behaviors Of The Stochastic Chemical Reaction Model Perturbed By White Noise

Dynamical behaviors of chemical reactions are the important parts of physical chemistry,which mainly study and reveal the rate and mechanism of chemical reaction.Since the early 1960 s,the phenomenon of sustained oscillations in biochemical reactions has been identified and has become an important part of experimental studies of biochemical reactions,so the use of mathematical models to study sustained oscillations has received increasing attention.Stochastic models are usually obtained by adding noise disturbances to a deterministic model.In fact,dynamical models of chemical reactions are always subject to the interference and influence of ambient white noise,so this paper focuses on the asymptotic behaviour of two types of stochastic chemical reactions subject to systematic disturbances,as follows:In the study of two kinds of stochastic glycolytic chemical reaction models,the Lyapunov analysis method is used to discuss their dynamic behavior.Firstly,it is proved that the system has a unique solution and the solution is positive globally,this is of great significance in chemical reactions.Secondly,by using Lyapunov analysis method,the stationary distribution and ergodicity of random glycolysis reaction system are obtained under certain conditions.It is interesting that the equilibrium points of deterministic chemical reaction models exhibit different behavior depending on the parameters.The stochastic system only needs white noise to satisfy a certain range,which can guarantee its stochastic ergodicity.Finally,the theoretical results obtained above are verified by numerical simulation.