中文摘要：

提出了一类基于比率Ivlev功能性反应且食饵有避难所的Leslie捕食-食饵系统.首先分析了常微分系统正平衡点的存在性和局部渐近稳定性,通过建立Dulac函数,得到常微系统正平衡点全局稳定的充分条件;其次,证明了在一定条件下,具有自扩散的偏微分系统会引起Turing不稳定;最后,利用MATLAB软件进行了数值模拟,并作出相应的分析.结果表明,在一定范围内,避难所的大小不改变常微分系统正平衡点的全局渐近稳定性.

英文摘要：

A ratio-dependent Leslie predator-prey system with Ivlev functional response incorporating a prey refuge was considered. Firstly, the existence and local asymptotic stability of the positive equilibrium of the ODE system were studied. Then, by constructing a suitable Dulac function, sufficient conditions were obtained for the global asymptotic stability of the positive equilibrium of the ODE system. Secondly, the PDE system with self-diffusion could induce the Turing instability in some conditions were proved. Finally, the numerical simulations by using Matlab were given to illustrate the main results and some corresponding discussions were presented. The results showed that, in a certain range, the refuge size has no influence on the global asymptotic stability of the positive equilibrium of the ODE system.