| This paper is to study qualitative properties of solutions to the Leslie-Gower predator-prey diffusion system with the prey refuge.The full text is divided into five chapters.The first chapter outlines the background.In the second chapter,we first study the dissipation,persistence and stability of non-negative constant steady states of system(1.4),If the assumption a2b1＞a1r2(1-m)2 holds,the system is persistent;Then,by constructing a suit-able Lyapunov function,we show that two non-negative constant steady states of the system are globally asymptotically stable for certain ranges of the param eters.ChapterⅢ,a priori upper and lower bounds for positive steady states of the system are established.ChapterⅣ,the nonexistence of nonconstant positive steady states of the system for certain ranges of the parameters.ChapterⅤ,by comparing the results between the system with the prey refuge and no refuge,we show that the prey refuge could influence the size of the attraction domain,but it has no influence on the stability of the system. |
