Study On The Dynamics Of Reaction-Diffusion Systems With Time-Varying Diffusivity

Time-varying diffusivity is a major factor for the reaction-diffusion system dynamics. And also it is the hot and difficult research point of pattern dynamics. In this paper, we comprehensively apply plural series and complex field theories and methods to derive the influence mechanism of time-varying diffusivity to reaction-diffusion system dynamics.It is divided into four chapters. The first chapter, we introduce the background and current situation of reaction-diffusion systems and pattern formation. And we briefly analyze the research of the Gray-Scott model and biological prey-predator system dynamics. Chapter II, firstly we give the appearing conditions of the saddle node bifurcation and B-T in the Gray-Scott model, we calculate the instability threshold value. On the basis, we utilize the series theory to certify the time-varying dynamics behavior with time-varying diffusivity linear function. Then we give the relevant of numerical analysis, and make corresponding the pattern formation. Chapter III, we analyze dynamics conduct in the model scale catches system with diffusivity cycle function. Firstly, we give the branch condition of Turing in the system. Then we derive that the system is more stability with diffusivity cycle function. At last, we give the corresponding numerical simulation and results. The fouth chapter of the paper, we make the conclusion and discuss of the study. The result will be help for studying on the dynamics of reaction-diffusion systems with time-varying diffusivity.