【作者】 李金仙；

【导师】 李胜家； 燕居让；

【作者基本信息】 山西大学 ， 基础数学， 2008， 博士

【摘要】 随着科学的发展，Lotka-Volterra系统和Gilpin-Ayala系统作为种群生态学中的两个经典模型，在自然科学和社会科学的很多学科中的重要性越来越突出，已发表大量的研究工作．本文分五章研究了上述两种系统的持久性，灭绝性或指数稳定性，所得结果改进并推广了相关已有的工作．第一章，介绍了所关注问题的研究背景和本文的主要工作．第二章，首先讨论了一类广义非自治N-种群Lotka-Volterra系统的强持久性，在此基础上，研究了经典的Lotka-Volterra系统并得到了系统部分持久与灭绝的充分条件，得到了若干新的结果，其中一些结果包含了原文献的工作．第三章，主要研究了具有时滞的Lotka-Volterra扩散系统给出了系统一致持久的充分条件．第四章，首先考虑了单种群扩散系统的一致持久性，在此基础上，又讨论了非线性捕食系统得到其若干持久性的充分条件．所得结果改进并推广了一些已有的结果。第五章，考虑了具有时滞变元的Lotka-Volterra模型的一致持久性和指数稳定性，建立了若干新的结果，改进并推广了一些已有结果．更多还原

【Abstract】 With the development of science, Lotka-Volterra system and Gilpin-Ayala system, as two basic models in population dynamics, play important roles in physical and social science. This thesis is composed of five chapters to consider the persistence, extinction or global exponential stability of above two systems. The results given in this paper improve and extend the corresponding ones in the literatures.In Chapter 1, we introduce the historical background of problems which will be investigated and the main works of this thesis.In Chapter 2, firstly the strong persistence of the following general nonautonomous Lotka-Volterra system is considered,By the above analysis, we consider the following Lotka-Volterra systemThe suficient conditions for the partial permanence and extinction of above system are obtained, which include the corresponding ones in the literatures.In Chapter 3, we mainly investicate in uniform persistence for a diffusive LotkaVolterrasystem with time delay,In Chapter 4, firstly we consider the following single species diffusive systemThe sufficient conditions for the uniform persistence of above system are obtained. Secondly, we propose the following nonlinear diffusive predator-prey systemsome sufficient conditions for the persistence of above system are obtained. Our results improve and extend the corresponding ones in the literatures.Chapter 5 is considered with a Lotka-Volterra system with time delaysome new sufficient conditions for permanence and exponential stability of above systemare obtained.更多还原