Qualitative Analysis For A Diffusive Predation-competition Model With A Prey Refuge

This paper is purported to study qualitative properties of solutions to the predation-competition reac-tion diffusion system with the prey refuge. The full text is divided into seven chapters. The first chapter outlines the background. In the second chapter, we can obtain local asymptotic stability of the unique pos-itive constant to system(1.7) by the eigenvalue function. Chapterâ…¢, a priori upper and lower bounds for positive steady states of the system are established. Chapterâ…£, we can obtain the global asymptotic stabil-ity of constant solutions to system (1.7) by constructing some suitable Lyapunov function. Chapterâ…¤, The non-existence results of non-trivial solution are derived. Chapterâ…¥, The existence results of non-trivial solution are derived.Chapterâ…¦, Conclusion.