Categories Based On The Reaction Diffusion Equations Of Dynamics Analysis Of Biological Systems

In the paper, we study the reaction-difusion epidemic models with diferent incidencerate and a predator-prey model, analysing the infuence of time-delay on the model andqualitative properties of the solutions of reaction-difusion equation and so on.Firstly we review some development of the related problems and summarize the mainwork in this thesis．Next we investigate the infuence of time-delay and difusion on theepidemic model, and obtain the critical value of delay. when delay is equal to the criticalvalue, the system produces Hopf branch; when delay is greater than its critical value, theperiodic solution appear. Then we study a reaction-difusion epidemic model with non-monotonic saturated incidence rate, and prove the dissipation, persistence and uniformlyasymptotically stability of the endemic equilibrium for the reaction-difusion system. Finallywe present a cubic predator-prey system with difusion. we obtain the condition that all thesolutions of the model uniformly tend to the equilibrium point, and prove the local andglobal stability of the nontrivial constant steady states.