带有脉冲的中立型捕食系统正周期解的存在性

发布时间：2018-11-05 15:01

【摘要】：种群动力系统是生物数学的重要研究方向,在对种群动力系统的研究中,学者们一般建立合适的数学模型结合相应的数学理论对复杂的生物系统的内在特征进行分析和研究.利用Mawhin连续性定理研究捕食系统的正周期解的存在性已经是非常有效的一种方法.本文主要运用Mawhin连续性定理和分析技巧,研究带有不同功能函数的捕食者与被捕食者模型正周期解的存在性.全文包括如下三章:第一章简要介绍研究的背景,意义及种群动力系统的几类基本的模型,并介绍了本文的主要工作.第二章研究带有脉冲和Holling IV型功能函数的中立型捕食与被捕食模型的正周期解的存在性,通过运用Mawhin连续性定理和分析技巧得到了模型的正周期解的存在性.第三章研究带有Beddington-DeAngelis型功能函数和脉冲时滞的多种群中立型捕食竞争系统,运用Mawhin连续性定理和分析技巧获得了该系统正周期解的存在性,推广了相关文献的主要结果.
[Abstract]:Population dynamic system is an important research direction in biological mathematics. In the study of population dynamic system, scholars generally establish appropriate mathematical models and corresponding mathematical theory to analyze and study the inherent characteristics of complex biological system. It is an effective method to study the existence of positive periodic solutions of predator-prey systems by using Mawhin continuity theorem. In this paper, the existence of positive periodic solutions for predator and prey models with different functional functions is studied by using Mawhin continuity theorem and analytical techniques. The thesis consists of three chapters as follows: chapter 1 briefly introduces the background, significance and several basic models of population dynamic system, and introduces the main work of this paper. In chapter 2, we study the existence of positive periodic solutions of neutral predator-prey model with impulsive and Holling IV type functional functions. By using Mawhin continuity theorem and analytical technique, we obtain the existence of positive periodic solutions of the model. In chapter 3, we study several group neutral predator-prey competition systems with Beddington-DeAngelis type function and impulsive delay. By using Mawhin continuity theorem and analytical technique, we obtain the existence of positive periodic solutions of the system, and generalize the main results of relevant literature.
【学位授予单位】：江苏师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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