Dynamics Of A Class Of Cooperative-Competitive Reaction-Diffusion Model

In this dissertation,we study the dynamical behavior of a kind of cooperativecompetitive reaction diffusion system based on sexually transmitted disease.Since two different strains and different behaviors of individuals are considered,the model involves four unknown functions.The purpose of this paper is to describe the possible substitution and coexistence of different strains.First,when the space domain is a bounded interval,we consider the long time behavior of the corresponding initial boundary value problem,in which the boundary condition is the mixed one.The main objective is to study the existence and stability of boundary and positive equilibrium such that we can analyze the competition,exclusion and coexistence of populations in bounded domains.With the help of monotone semiflow theory,eigenvalue theory,upper and lower solution methods and other techniques,the existence and stability of non-constant boundary equilibrium and positive equilibrium are obtained under proper sufficient conditions.These results correspond to different extinction and persistent phenomena of two strains.Second,when the space variable is the whole real axis,the propagation threshold of the cooperative-competitive reaction-diffusion system is studied.The main purpose is to describe the competitive exclusion process of two different strains.Making proper linear transformation,a cooperative system can be obtained.However,the corresponding cooperative system is not always subhomogeneous and the invariant region is not always rectangular,which leads to some difficulties in the theoretical analysis.With the help of the propagation theory of monotone semiflows,the unique propagation threshold is obtained.Then,by constructing an appropriate upper solution,it is proved that the threshold is linearly selected under certain conditions.Because the threshold is unique,numerical simulation becomes a possible method to show the propagation properties.Through some numerical examples,we observe some phenomena that not only illustrates the linear selection but also indicates the nonlinear selection of propagation threshold.