具有不同时刻脉冲控制和Holling Ⅱ功能反应的离散捕食-被捕食模型动力学行为

摘要

利用分段欧拉法建立一类具有不同时刻脉冲控制和Holling Ⅱ功能反应的离散捕食-被捕食模型,并对该模型进行分析.借助于Floquest定理,证明当周期T小于某个临界值时,害虫灭绝周期解的存在性及全局渐近稳定性.当周期T大于某个临界值时,离散系统的解是永存的.数值算例验证了所得结论的正确性.%A discrete Holling type Ⅱ predator-prey model with impulsive control strategy at different fixed times is proposed by using the piecewise Euler method,and some analysis is further given.By the help of Floquets theorem,the existence and globally asymptotic stability of pest-eradication periodic solution are investigated when the impulsive period is less than some critical value.It is shown that the solution of discrete system is permanence if the impulsive period is larger than some critical value.Some numerical experiments are offered to justify the correctness of theoretical results.