具有避难所的非自治差分修正Leslie-Gower捕食-食饵系统的动力学行为研究
Dynamics of a nonautonomous discrete Leslie-Gower predator-prey system with a prey refuge

研究一类具有避难所的非自治差分修正Leslie-Gower捕食-食饵系统，通过对系统动力学行为的详细分析，得到保证系统持久和全局渐近稳定的充分性条件，发现只要避难所足够大就可以保证食饵种群持久生存. 借助差分不等式获得一组保证食饵种群绝灭而捕食者种群持久的充分性条件，发现当避难所较小时，食饵种群会由于捕食者的捕食而最终绝灭，但此时捕食者由于拥有其他的食物来源仍可持久生存.
A nonautonomous discrete modified Leslie-Gower predator-prey system incorporating a prey refuge is studied in this paper. Sufficient conditions which guarantee the permanence and global stability of the system are obtained. Our results show that enough large prey refuge could keep the system persistent. We also show that prey will be driven to extinction if prey refuge is too small，however predator species still keep persistent due to the other food resource