【作者】 陈福来；

【导师】 文贤章；

【作者基本信息】 湖南师范大学 ， 基础数学， 2004， 硕士

【摘要】 本文研究脉冲泛函微分方程的渐近稳定性及脉冲作用下种群模型的周期解。 在第二章，研究脉冲泛函微分方程的渐近稳定性，建立了脉冲泛函微分方程零解的渐近稳定性和一致渐近稳定性定理，得到的结果推广或改进了相关的结果。 借助重合度理论这一工具，在第三章，研究具有脉冲和无穷时滞的捕食-食饵系统的正周期解的存在性；在第四章，研究具有脉冲和时滞的Lotka-Volterra系统的正周期解的存在性和全局渐近稳定性；在第五章，研究脉冲中立型单种群模型海南师范大学硕士学位论文的正周期解的存在性，分别得到了一些充分条件.更多还原

【Abstract】 In this paper,we study the asympotic stability for impulsive functional differential equation and periodic solutions of population models influenced by impulses.In chapter two,we study the asympotic stability for impulsive functional differential equation:and establish the asympotic stability theorems and the uniformly asympotic stability theorems of zero solutions of the impulsive functional differential equation, the theorems extend or improve the former results.By using the method of coincidence degree,in chapter three,we study the existence of positive periodic solution of Predator-Prey system with impulses and infinite delay:in chapter four,we study the existence and global asymptotic stability of the positive periodic solution of a Lotka-Volterra system with delays and impulses:in chapter five,we study the existence of positive periodic solution of a impulsive neutral modal of single-species population growth:and respectively obtain some new sufficient conditions.更多还原