具有脉冲和斑块效应的种群周期系统的稳定性与持久性

发布时间：2018-05-04 16:18

本文选题：脉冲扩散 + 周期环境　；参考：《重庆师范大学》2017年硕士论文

【摘要】：在生态环境中,种群的扩散和迁徙是一个很普遍的现象,且在实际生活中种群的数量变化会受到天气、季节等因素的影响,因此考虑周期环境下具有脉冲效应的种群模型更具有实际意义.另外,利用脉冲微分方程来描述种群动力学的脉冲效应,如害虫治理、捕捞、免疫等成为研究热点.基于此,本文分别考虑在脉冲控制下的单斑块和多斑块的周期系数种群模型,给出害虫灭绝周期解的稳定性与持久性条件.全文主要分为两个部分:第一部分主要考虑在不同脉冲时刻收割庄稼、喷洒农药以及释放天敌等因素,研究具有周期系数的脉冲种群控制模型.利用脉冲微分方程比较原理、线性化方法以及Floquet原理,得到系统的害虫灭绝周期解的局部渐近稳定性和全局渐近稳定性的充分条件.第二部分研究在斑块环境下具有周期系数的植物害虫天敌脉冲控制模型.在第一部分模型的基础上,考虑种群的扩散性,将单斑块模型推广到m-斑块模型,同时考虑在不同脉冲时刻进行收割庄稼、喷洒农药以及释放天敌.利用脉冲微分方程比较原理、线性化方法以及Floquet原理,我们得到系统害虫灭绝周期解全局渐近稳定性的充分条件.然后通过持久性理论得到该系统的持久性条件.最后给出2个斑块情况下的数值例子,从而验证所得结论.
[Abstract]:In the ecological environment, population diffusion and migration is a very common phenomenon, and in real life, the number of population changes will be affected by weather, season and other factors, Therefore, it is more meaningful to consider the population model with pulse effect in periodic environment. In addition, impulsive differential equations are used to describe the impulsive effects of population dynamics, such as pest control, fishing, immunity and so on. Based on this, the periodic coefficient population models of single and multiple patches under impulsive control are considered, respectively, and the stability and persistence conditions of the periodic solutions of pest extinction are given. The paper is divided into two parts: in the first part, the pulse population control model with periodic coefficient is studied by considering the factors of harvesting crops at different pulse times, spraying pesticides and releasing natural enemies. By using the comparison principle of impulsive differential equations, linearization method and Floquet principle, sufficient conditions for the local asymptotic stability and global asymptotic stability of the periodic solution of pest extinction are obtained. In the second part, the pulse control model of natural enemies of plant pests with periodic coefficient in patch environment is studied. Based on the first part of the model, considering the diffusion of population, the single patch model is extended to m- patch model. At the same time, harvesting crops, spraying pesticides and releasing natural enemies at different pulse times are considered. By using the comparison principle of impulsive differential equations, linearization method and Floquet principle, we obtain sufficient conditions for the global asymptotic stability of the periodic solution of pest extinction. Then the persistence condition of the system is obtained by persistence theory. Finally, numerical examples of two patches are given to verify the results.
【学位授予单位】：重庆师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

【参考文献】