污染水体中捕食种群具有常数投放率的脉冲状态反馈控制模型
Impulsive State Feedback Control Model of Predator Population with Constant Release Rate in Polluted Water
摘要: 水体富营养化引起的破坏水生生态系统的现象时有发生，本文研究了污染水体中捕食种群具有常数投放率和脉冲状态反馈控制的食饵捕食系统。通过构造李雅普诺夫函数得到了系统在无脉冲效应的情况下全局渐近稳定的充分条件。利用半连续动力系统的几何理论和后继函数方法，得到了脉冲作用下系统具有阶一周期解，且得到了阶一周期解具有存在和唯一性。最后，通过数值模拟来说明我们的理论结果及生物学意义。
Abstract: The destruction of aquatic ecosystems caused by eutrophication of water bodies occurs from time to time. In this paper, a predator-prey system with constant release rate and impulsive state feedback control of predator population in polluted water is studied. By constructing Lyapunov function, a sufficient condition for the global asymptotic stability of the system without impulse effect is ob-tained. By using the geometric theory of semi-continuous dynamic system and the successor func-tion method, it is obtained that the system has order-1 periodic solution under the action of impulse, and the existence and uniqueness of order-1 periodic solution are obtained. Finally, we illustrate our theoretical results and biological significance by numerical simulation.
文章引用：王秀秀, 张蒙. 污染水体中捕食种群具有常数投放率的脉冲状态反馈控制模型[J]. 应用数学进展, 2022, 11(10): 7302-7311. https://doi.org/10.12677/AAM.2022.1110775

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