【作者】 张迪；

【导师】 张慧星；

【作者基本信息】 中国矿业大学 ， 基础数学， 2018， 硕士

【摘要】 自然界中很多生命现象的发生及对种群的优化控制和管理并不是一个连续的过程,不能单纯地用微分方程或差分方程来描述.因此,脉冲微分系统作为一种特殊的不连续系统,被广泛地用来分析生物数学中种群数量的变化规律及解释客观现象.用此系统来解决种群动力学行为,可以帮助我们更好的理解自然界中种群的变化规律并解释复杂的生物现象.本文运用Mawhin连续性定理研究带有脉冲及不同功能反应函数的几类种群模型正周期解的存在性问题.全文共分为四章,具体内容安排如下:第一章是绪论部分,主要介绍课题的研究背景意义、研究现状、本文的主要工作及创新点.第二章利用Mawhin连续性定理,首先研究了带有脉冲和Holling type Ⅲ比率依赖的中立型捕食食饵模型,在中立项的时滞小于等于零的情况下得到其正周期解的存在性,其次研究了在脉冲和时滞影响下的Lotka-Volterra捕食食饵模型,并得到其正周期解的存在性.第三章利用Mawhin连续性定理研究脉冲及中立项影响下的时滞捕食食饵模型,且得到模型多个正周期解的存在性.第四章是总结本文主要工作及对以后的研究探讨进行展望.更多还原

【Abstract】 In nature,the occurrence of many life phenomena and the optimal control and man-agement of populations are not a continuous process and cannot be described simply by differential equations or difference equations.Therefore,as a special discontinuous sys-tem,the pulse differential system is widely used to analyze the changes of the population quantity in biological mathematics and to explain the objective phenomena.The behavior of population dynamics can help us better understand the natural population changes and explain complex biological phenomena.In this thesis,by using Mawhin’s continuation theorem,we study the existence of positive periodic solutions for several kinds of popu-lation models with impulses and different functional response functions.The full text is divided into four chapters,the specific contents are arranged as follows:Chapter one mainly introduces the research background,research status,the main work and innovation of this paper.In chapter two,firstly,we consider a neutral predator-prey model with impulsive and Holling Ⅲ ratio-dependent predator-prey models,under the condition that the time delay of the neutral term is less than or equal to zero.Secondly,Lotka-Volterra predator-prey model with impulsive delays is discussed.By using Mawhin’s continuation theorem,the existence of positive periodic solutions is obtained.In chapter three,we study the predator-prey model with time delay under the influence of impulsive and neutral terms,and apply Mawhin’s continuation theorem to obtain the existence of multiple positive periodic solutions.In chapter four,we summarize the main work of this paper and look forward to future research.更多还原