Qualitative Analysis For A Ratio-dependent Predator-prey Model With Disease And Diffusion

This paper is purported to study a reaction diffusion system arising from a ratio-dependent predatorprey model with disease.The full text is divided into five sections.The first section outlines the background.In the second section,we study the large time behavior of time-dependent solutions for(1.6),If the assumption kl＞b₁,1-b₂-(l/m)＞0 holds,the system is permanent.Sectionâ…¢,we can obtain the global asymptotic stability of semi-trivial solutions by constructing some suitable Lyapunov function.Then,by the eigenvalue function,the local asymptotic stability of the unique positive constant can obtained.Sectionâ…£,we can get the bounds for positive steady state of the corresponding elliptic system of(1.6).Sectionâ…¤,The non-existence results of non-trivial solution are derived.