Permanence, stability, and coexistence of a diffusive predatora??prey model with modified Lesliea??Gower and Ba??D functional response

摘要

This paper investigates a diffusive predatora??prey system with modified Lesliea??Gower and Ba??D (Beddingtona??DeAngelis) schemes. Firstly, we discuss stability analysis of the equilibrium for a corresponding ODE system. Secondly, we prove that the system is permanent by the comparison argument of parabolic equations. Thirdly, sufficient conditions for the global asymptotic stability of the unique positive equilibrium of the system are proved by using the method of Lyapunov function. Finally, by using the maximum principle, Poincare inequality, and Leraya??Schauder degree theory, we establish the existence and nonexistence of nonconstant positive steady states of this reaction-diffusion system, which indicates the effect of large diffusivity.