有干扰影响的脉冲捕食—食饵系统的稳定性研究与数值分析
发布时间：2018-08-22 20:49
【摘要】：随着社会的发展与生态环境的破坏,生态系统的稳定性研究日益受到人们的重视.由于生态环境的复杂性,在实践中研究生态系统的稳定性时,往往需要考虑种群相互干扰以及人为的脉冲控制等因素的影响.本文主要研究三类捕食者相互干扰的脉冲捕食-食饵系统的稳定性问题,主要由以下五章构成.第一章主要介绍本文的研究背景、研究意义以及国内外研究现状等.第二章是预备知识介绍,主要给出证明系统有界性、食饵灭绝周期解存在性及其全局渐近稳定性、持久性相关的定义和主要引理.第三章主要研究了一类捕食者相互干扰的脉冲捕食-食饵系统的稳定性问题.应用脉冲微分方程稳定性理论、生物系统理论,通过比较的方法,研究得到了食饵灭绝周期解的存在性及其全局渐近稳定性,以及系统持久的充分条件.然后通过数值模拟对系统的稳定性做数值分析,进一步探讨系统复杂的动力学行为.最后从生物理论的角度出发,分析了所得结果的生物意义,给出一些可行的系统控制策略与建议.第四章主要考虑了一类具有平方根功能反应函数、捕食者之间相互干扰的脉冲三种群捕食—食饵模型.通过利用脉冲扰动技巧、弗洛凯理论、不等式理论、比较定理等基本理论,研究了该系统食饵灭绝周期解的存在性、全局渐近稳定性的充分条件.通过构建适当的Lyapunov函数,采用比较的方法,进一步讨论得到了系统持久的充分条件.最后通过数值模拟讨论了干扰系数、脉冲周期等对系统稳定性的影响,揭示了系统复杂的动力学性质.第五章主要从实际出发,考虑到不同时刻有化学控制和生物控制、捕食者之间有相互干扰等因素对种群的实际影响,建立了一类脉冲三物种捕食-食饵模型.利用相关理论主要研究得到了食饵灭绝和系统持久的充分条件.然后举例并进行数值模拟,进一步研究了系统的动力学性质.最后通过讨论给出了所得结果的生物意义,结合相关控制策略给出了一些具体的意见与建议.总之,通过对上述系统的理论分析,得到了系统周期解的存在性、系统的稳定性、系统的持久性等系列理论成果,所得结果推广或改进了一些已有的理论结果,丰富了脉冲微分系统和生物动力系统理论.通过数值模拟,进一步研究了干扰因素、脉冲因素、功能反应等对系统动力学性质的广泛影响,进一步揭示了系统复杂的动力学性质,为系统控制与生态平衡保护等给出了一些控制策略与建议.所得成果有较好的理论意义和一定的实际意义.
[Abstract]:With the development of society and the destruction of ecological environment, people pay more and more attention to the study of ecosystem stability. Because of the complexity of ecological environment, when studying the stability of ecosystem in practice, it is necessary to consider the influence of population interferences and artificial impulse control. In this paper, the stability of impulsive predator-prey systems with three kinds of predator interferences is studied, which consists of the following five chapters. The first chapter mainly introduces the research background, research significance and domestic and foreign research status. The second chapter is the introduction of preparatory knowledge, which mainly gives the definitions and main lemmas to prove the boundedness of the system, the existence of the periodic solution of prey extinction and its global asymptotic stability, the permanence correlation. In chapter 3, the stability of a class of impulsive predator-prey systems with predator interferences is studied. By using the theory of stability of impulsive differential equations and the theory of biological systems, the existence and global asymptotic stability of the periodic solutions of prey extinction are studied by means of comparative methods, and the sufficient conditions for the permanence of the systems are obtained. Then the stability of the system is analyzed by numerical simulation, and the complex dynamic behavior of the system is further discussed. Finally, the biological significance of the results is analyzed from the point of view of biological theory, and some feasible system control strategies and suggestions are given. In chapter 4, we consider a class of impulsive three-species predator-prey model with square root function and predator interaction. By using the impulsive perturbation technique, Flokay theory, inequality theory, comparison theorem and other basic theories, the sufficient conditions for the existence and global asymptotic stability of the perishing periodic solution of the system are studied. By constructing the proper Lyapunov function and adopting the method of comparison, the sufficient conditions for the persistence of the system are obtained. Finally, the effects of disturbance coefficient and pulse period on the stability of the system are discussed by numerical simulation, and the complex dynamic properties of the system are revealed. In the fifth chapter, considering the effects of chemical and biological control at different times and the interaction between predators on the population, a class of impulsive three-species predator-prey model is established. The sufficient conditions of prey extinction and system persistence are obtained by using relevant theories. The dynamic properties of the system are further studied by numerical simulation. Finally, the biological significance of the obtained results is discussed, and some specific suggestions and suggestions are given based on the related control strategies. In a word, the existence of periodic solution, the stability of the system and the persistence of the system are obtained through the theoretical analysis of the above mentioned systems. The results extend or improve some existing theoretical results. It enriches the theory of impulsive differential system and biodynamic system. Through numerical simulation, the extensive influence of disturbance factors, pulse factors and functional reactions on the dynamic properties of the system is further studied, and the complex dynamic properties of the system are further revealed. Some control strategies and suggestions are given for system control and ecological balance protection. The obtained results have good theoretical and practical significance.
【学位授予单位】：桂林理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
本文编号：2198259
[Abstract]:With the development of society and the destruction of ecological environment, people pay more and more attention to the study of ecosystem stability. Because of the complexity of ecological environment, when studying the stability of ecosystem in practice, it is necessary to consider the influence of population interferences and artificial impulse control. In this paper, the stability of impulsive predator-prey systems with three kinds of predator interferences is studied, which consists of the following five chapters. The first chapter mainly introduces the research background, research significance and domestic and foreign research status. The second chapter is the introduction of preparatory knowledge, which mainly gives the definitions and main lemmas to prove the boundedness of the system, the existence of the periodic solution of prey extinction and its global asymptotic stability, the permanence correlation. In chapter 3, the stability of a class of impulsive predator-prey systems with predator interferences is studied. By using the theory of stability of impulsive differential equations and the theory of biological systems, the existence and global asymptotic stability of the periodic solutions of prey extinction are studied by means of comparative methods, and the sufficient conditions for the permanence of the systems are obtained. Then the stability of the system is analyzed by numerical simulation, and the complex dynamic behavior of the system is further discussed. Finally, the biological significance of the results is analyzed from the point of view of biological theory, and some feasible system control strategies and suggestions are given. In chapter 4, we consider a class of impulsive three-species predator-prey model with square root function and predator interaction. By using the impulsive perturbation technique, Flokay theory, inequality theory, comparison theorem and other basic theories, the sufficient conditions for the existence and global asymptotic stability of the perishing periodic solution of the system are studied. By constructing the proper Lyapunov function and adopting the method of comparison, the sufficient conditions for the persistence of the system are obtained. Finally, the effects of disturbance coefficient and pulse period on the stability of the system are discussed by numerical simulation, and the complex dynamic properties of the system are revealed. In the fifth chapter, considering the effects of chemical and biological control at different times and the interaction between predators on the population, a class of impulsive three-species predator-prey model is established. The sufficient conditions of prey extinction and system persistence are obtained by using relevant theories. The dynamic properties of the system are further studied by numerical simulation. Finally, the biological significance of the obtained results is discussed, and some specific suggestions and suggestions are given based on the related control strategies. In a word, the existence of periodic solution, the stability of the system and the persistence of the system are obtained through the theoretical analysis of the above mentioned systems. The results extend or improve some existing theoretical results. It enriches the theory of impulsive differential system and biodynamic system. Through numerical simulation, the extensive influence of disturbance factors, pulse factors and functional reactions on the dynamic properties of the system is further studied, and the complex dynamic properties of the system are further revealed. Some control strategies and suggestions are given for system control and ecological balance protection. The obtained results have good theoretical and practical significance.
【学位授予单位】：桂林理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
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