水体富营养化状态脉冲控制系统周期解的存在性和唯一性

Existence and Uniqueness of Periodic Solution of a State-dependent Impulsive Control System on Water Eutrophication

本文基于藻类治理问题,建立了一个具有状态依赖脉冲和Holling I型功能性反应函数的藻类治理模型,利用常微分方程的定性理论和Lambert W函数以及Poincare映射的性质研究了系统阶1周期解的存在性和唯一性.最后,通过数值模拟对文中主要结论进行了验证.

In this paper, a state-dependent impulsive model is proposed for the algae control, which involves state-dependent impulse and Holling type I funetional response function. We investigate the existence and uniqueness of order 1 periodic solution of the system by using the qualitative theory of ordinary differential equation and the properties of the Lambert W flmction and Poincare map. Finally, numerical simulations are carried out to illustrate the theoretical results.