研究了一类具有庇护所的两种群捕食-食饵模型,其功能函数为HollingⅡ型.首先,利用抛物型方程的比较原理探究了模型正解的耗散性和一致持久性;其次,利用稳定性理论得到了常数解的渐进稳定性条件;最后,利用Lyapunov函数给出了常数解的全局稳定条件.
In this paper,the predator-prey model with Holling type Ⅱ functional response incorporating a prey refuge is studyed. Firstly, the asymptotic behavior of spatially inhomogeneous solutions is investigated according to the comparison argument for parabolic problem. Secondly, by the linearized stability theory, the locally asymptotically stability of positive constant steady-state solution is discussed. Finally, the globally asymptotically stability of positive constant steady-state solution is established using a Lyapunov function.