一类具有避难所的脉冲捕获系统的研究

讨论了一类具有避难所和脉冲捕获的捕食系统．因为食饵种群具有避难所，所以在一定条件下可以使捕食者灭绝，即当脉冲周期小于某一临界值时，存在全局稳定的捕食者灭绝周期解，脉冲周期增大至大于临界值时，平凡捕食者灭绝周期解失去稳定性并产生正周期解，利用分支理论研究正周期解的存在性．进而，利用比较定理等方法确定了持续生存的条件．

Study on A Kind of Impulsive Harvested System with Refuges

A kind of system with refuges and impulsive harvest is discussed in this paper.Because prey species have refuges,predator may be extinct under some conditions.There exists a global stable predator eradication period solution when the impulsive period is less than a certain critical value.When the impulsive period increase,the trivial periodic predator-eradication solution loses its stability and a positive periodic solution comes out.Then the existence of the positive periodic solution is studied by the bif...