具有相互干扰的一个捕食者两个食饵系统的综合害虫治理

摘要

Taking into account chemical control, biological control for pest management at different fixed moments, and the mutual interference of the predator, we propose in this paper a three-species predator-prey system with chemical control, biological control and mutual interference of predator. Based on the theory of impulsive equa-tion, small amplitude perturbation and Floquet theory, we investigate the existence and globally asymptotic stability of the prey-eradication periodic solution for this system. By using comparison methods involving multiple Lyapunov functions, some su?cient conditions assuring the permanence of this system are obtained. Some ex-amples and numerical simulations are given to show the complex behaviors of this system. Further, the biological implications of our main results are analyzed and some suggestions for feasible control strategies are given.%考虑到固定时刻化学控制、生物控制及捕食者有相互干扰等因素的影响,本文构建了一个具有生物控制、化学控制及捕食者有干扰影响的三种群捕食-食饵系统.利用脉冲微分理论、小振幅扰动理论和弗洛凯理论,研究了该系统有关食饵灭绝周期解的存在性和全局渐进稳定性等性质.利用比较定理,通过构造适当的李雅普诺夫函数,讨论得到系统持续生存的充分条件.然后通过举例并进行数值模拟进一步讨论了系统复杂的动力学性质.最后分析讨论了所得结果的生物意义并从害虫综合控制角度给出了一些合理的意见与建议.