Kinetic Behavior Analysis Of A Class Of Reaction-diffusion Models

The two-species competition model is widely used to investigates the dynamical process of competition among ecological species,and to explore the resource conditions for their survival and growth.The dissertation deals with the following two-species competition model,which describing the interaction of resource distributions and diffusion strategies:Firstly,The effect of diffusion coefficient on the dynamical behavior of the model is investigated.With the help of the related eigenvalue problems,the critical dynamical behavior of the model is obtained,which is based on the eigenvalue theory and the monotone dynamical system theory.Moreover,the sufficient conditions for species coexistence or extinction are presented.The corresponding results indicate that the diffusion strategy affects the principal eigenvalue,which directly have an impact on the dynamical behavior of the system.Secondly,combining the eigenvalue problem corresponding to the above model by taking the inter-specific competition coefficients as the parameters,the critical values on the inter-specific competition coefficients are obtained.In addition,the existence and stability of the semi-trivial steady-state solutions and positive equilibrium solutions of the system are studied by using the eigenvalue theory and the elliptic regularity theory.We study the non-existence of the co-existence steady state solutions when one of the inter-specific competition coefficients is sufficiently large,and the other inter-specific competition coefficient is less than the corresponding critical inter-specific competition coefficient.Furthermore,the competition exclusion principle holds.That is,the species whose the competition coefficient does not exceed the corresponding critical value will be eliminated in the competition.Finally,in terms of these critical values,the structure and stability of bifurcation branches of positive equilibriums arising from two semi-trivial steady states are given by means of the bifurcation theory.In addition,the local bifurcation solution is extended to the global bifurcation solution.