一类相异功能反应的predator-prey扩散系统的稳定性

Stability of a predator-prey diffusion system with different functional response

针对斑块生境下具有庇护所效应的相异功能性反应predator-prey扩散系统,讨论了系统持续生存的条件.运用常微分方程定性理论讨论了系统解的有界性,通过构造Lyapunov函数得到了一定条件下该系统正解是全局渐近稳定的.进一步利用Pioncare定理和Brower定理证明了惟一周期正解的存在性与稳定性.

A predator-prey diffusion system between patches,which prey takes different functional response between different patches,and prey has refuge in a patch is studied.The condition of persistence is discussed.The boundedness of the solution of the system is given by qualitative theory of ordinary differential equations.Then positive solution is proved to be globally asymptotically stable by means of Lyapunov function.Furthermore,the only periodic positive solution is proved to be of existence and stable by using the Pioncare theorem and fixed point theorem.