几类具有脉冲作用的捕食模型的研究

发布时间：2018-05-31 20:36

本文选题：捕食模型 + 脉冲出生　；参考：《山西师范大学》2015年硕士论文

【摘要】：本文研究了几类具有脉冲作用的捕食模型的动力学性质,全文共分为三章：第一章,绪论,介绍了本文的研究背景,主要工作以及所用到的预备知识.第二章：建立并研究了污染环境中具有脉冲出生和收获的捕食模型,利用频闪映射得到了捕食者灭绝周期解的充分条件.进一步,讨论了捕食者灭绝周期解的全局吸引性和系统的持久性,并得到了阈值条件.这些理论为保护种群免于在污染环境中灭绝提供了可靠的理论依据.最后本章给出数值模拟来验证理论结果的正确性.第三章,建立并研究了具有脉冲扩散和脉冲收获的单种群模型.利用由频闪映射得到的离散动力学系统,得到了一个正不动点并且当种群的捕获量小于某一值或脉冲周期大于某一值时这个正不动点是全局稳定的.相应地,这个具有脉冲扩散和脉冲收获的单种群系统有一个全局稳定的正周期解.最后本章给出数值模拟来验证理论结果的正确性.第四章,建立并研究了一类具有B-D功能性反应函数的捕食者有病的捕食模型,该模型考虑了基于食饵的一个固定比例的避难所,它为食饵提供了一个免于被捕食的生存环境.通过对系统的定性分析得到了模型平衡点的存在性与稳定性的充分条件.进一步：利用比较定理得到了系统持久性的充分条件.最后本章给出数值模拟来验证理论结果的正确性.
[Abstract]:In this paper, the dynamic properties of several predatory models with impulsive action are studied. The whole paper is divided into three chapters: chapter one, introduction. The background, main work and the preparatory knowledge used in this paper are introduced. Chapter 2: the predator model with impulsive birth and harvest in polluted environment is established and studied. The sufficient conditions for the periodic solution of predator extinction are obtained by stroboscopic mapping. Furthermore, the global attractiveness of the periodic solution of predator extinction and the permanence of the system are discussed, and the threshold conditions are obtained. These theories provide a reliable theoretical basis for protecting populations from extinction in polluted environment. Finally, numerical simulation is given to verify the correctness of the theoretical results. In chapter 3, a single population model with pulse diffusion and pulse harvesting is established and studied. Using the discrete dynamical system derived from stroboscopic mapping, a positive fixed point is obtained and the positive fixed point is globally stable when the population catch is less than a certain value or the pulse period is greater than a certain value. Accordingly, the single-species system with impulsive diffusion and impulsive harvesting has a globally stable positive periodic solution. Finally, numerical simulation is given to verify the correctness of the theoretical results. In chapter 4, a predator-diseased predator model with B-D functional response function is established and studied. The model considers a fixed-scale shelter based on prey, which provides a living environment free from prey. The sufficient conditions for the existence and stability of the equilibrium point of the model are obtained by qualitative analysis of the system. Furthermore, the sufficient conditions for the persistence of the system are obtained by using the comparison theorem. Finally, numerical simulation is given to verify the correctness of the theoretical results.
【学位授予单位】：山西师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O175

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