Qualitative Analysis Of Prey-predator Model With Holling-Ⅳ Type Function Response And Diffusion

This thesis mainly investigates the dynamical behaviors of reaction-diffusion prey-predator systems with the toxin-determined functional response and general Holling type-Iv functional response by applying the qualitative and stability theory of ordinary differential equations, the theory of nonlinear functional analysis and the theory of nonlinear partial differential equations. The whole thesis is divided into four chapters.The first chapter is the introduction. The development of reaction-diffusion equa-tion is summarized and the problem studied in the present thesis is proposed.The second chapter is the preliminaries and we give the main definitions and re-lated lemma used in this paper.The third chapter considers the reaction-diffusion prey-predator model with the toxin-determined functional response and subject to Neumann boundary condition. The local asymptotic stability condition of the constant steady-state solution is ob-tained and it is found that the spatial diffusion has no any effect on the stability of the equilibria of the local system. In addition, the global asymptotic stability of a feasible constant positive steady state is studied and the conditions under which non-constant steady-state solution do not exist are also obtained. Finally, Hopf bifurcation of the system at the constant positive steady state is considered.The fourth chapter first is concerned with the reaction-diffusion predator-prey model with the general Holling-IV type functional response-diffusion..