几类种群模型的定性性质

发布时间：2018-04-12 10:36

本文选题：脉冲 + 时滞　；参考：《湖南科技大学》2017年硕士论文

【摘要】：种群动力学通常是通过数学建模的方法构建种群模型,用种群动力学的知识解释一些生态现象,研究生命科学的规律.本文以种群模型为研究对象,讨论了带有脉冲函数的时滞Nicholson飞蝇模型与时滞捕食模型的动力学性质.主要内容包括:(1)研究了一类非线性脉冲时滞的Nicholson飞蝇模型,使用微分方程的比较原理得到了该模型一致持久的充分条件.在此基础上,利用重合度原理,得到系统正周期解的存在性.(2)研究了一类非自治密度依赖的时滞捕食模型的动力学行为.运用微分方程比较原理,获得该模型一致持久的充分条件.通过使用Lyapunov函数,进一步证明了该系统的全局吸引性和正周期解的唯一性.
[Abstract]:Population dynamics usually uses mathematical modeling method to construct population model, explain some ecological phenomena with the knowledge of population dynamics, and study the law of life science.In this paper, the dynamic properties of the delayed Nicholson fly model and the delayed predator model with impulsive function are discussed.The main contents include: 1) A class of nonlinear impulsive time-delay Nicholson fly model is studied. By using the comparison principle of differential equations, sufficient conditions for the consistency and persistence of the model are obtained.On this basis, by using the coincidence degree principle, we obtain the existence of positive periodic solutions of the system. We study the dynamic behavior of a class of nonautonomous density-dependent delay-predator-prey models.By using the comparison principle of differential equations, a sufficient condition for uniform persistence of the model is obtained.By using the Lyapunov function, the global attractivity and the uniqueness of the positive periodic solution of the system are further proved.
【学位授予单位】：湖南科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

【参考文献】