Dynamic Behaviors Of The Stochastic Biochemical Reaction Models Perturbed By White Noise

The chemical reaction dynamics is a branch of physical chemistry, which s-tudy on chemical process and reaction rate. The first mathematical model predicts sustained oscillation is Lotka model. Since the beginning of 1960s, due to the sustained oscillations were founded in biochemical reaction, they have become an important part of the experimental research. People pay more and more atten-tion to the method of mathematical model. Since biochemical reaction model is affected by environmental white noise inevitably, so this paper mainly studies the asymptotic behavior of several kinds of stochastic model in biochemical reaction under the perturbation on system or parameter, main contents are:1. Study on stochastic trimolecular chemical reaction system. The first part discusses the dynamics of stochastic low concentration trimolecular chemical reac-tion model, we obtain the solution of the system is positive and global, and there is the stationary distribution and ergodicity under certain conditions. The second part discusses the dynamic behavior of the stochastic Oregonator chemical reac-tion model when we added the multiplicative noise as the express of environmental white noise, and then the existence and uniqueness of positive solutions and the ergodicity of the stochastic model are proved.2. Study on stochastic multi-molecular chemical reaction system. The first part is about the dynamics of a stochastic multi-molecular biochemical reaction model. At first, we proved the existence and uniqueness of positive solutions of the system. And then, for stochastic systems, we obtain the conditions when the reaction will end and when the reaction being proceed. Furthermore, we discuss the asymptotic behavior of the system around the equilibrium P*. The second part discuss the long time behavior of the negative feedback enzymatic reaction model under the disturbance of white noise, and we get the existence and uniqueness of positive solutions and the ergodicity of the system.3. Study on random continuous stirred tank reactor system. The first part discuss the long-time behavior of a continuous stirred tank reactor model under the perturbation of white noise. In addition to prove the existence and uniqueness of positive solution, the main work in this part work is to discuss whether the stochastic CSTR model has the stationary distribution or it is ergodic. For the diffusive term of the stochastic system is degraded, the stationary distribution and the ergodicity of the random system is proved by the application of Markov semi-group theory. The second part study on the dynamic behaviors of a continuous stirred tank reactor model with the linear perturbation, and the asymptotic prop-erty, i.e. the existence and uniqueness of the positive solution and the ergodicity, of the random CSTR model with linear perturbation.