發(fā)布時間：2018-08-22 20:49

【摘要】：隨著社會的發(fā)展與生態(tài)環(huán)境的破壞,生態(tài)系統(tǒng)的穩(wěn)定性研究日益受到人們的重視.由于生態(tài)環(huán)境的復(fù)雜性,在實踐中研究生態(tài)系統(tǒng)的穩(wěn)定性時,往往需要考慮種群相互干擾以及人為的脈沖控制等因素的影響.本文主要研究三類捕食者相互干擾的脈沖捕食-食餌系統(tǒng)的穩(wěn)定性問題,主要由以下五章構(gòu)成.第一章主要介紹本文的研究背景、研究意義以及國內(nèi)外研究現(xiàn)狀等.第二章是預(yù)備知識介紹,主要給出證明系統(tǒng)有界性、食餌滅絕周期解存在性及其全局漸近穩(wěn)定性、持久性相關(guān)的定義和主要引理.第三章主要研究了一類捕食者相互干擾的脈沖捕食-食餌系統(tǒng)的穩(wěn)定性問題.應(yīng)用脈沖微分方程穩(wěn)定性理論、生物系統(tǒng)理論,通過比較的方法,研究得到了食餌滅絕周期解的存在性及其全局漸近穩(wěn)定性,以及系統(tǒng)持久的充分條件.然后通過數(shù)值模擬對系統(tǒng)的穩(wěn)定性做數(shù)值分析,進一步探討系統(tǒng)復(fù)雜的動力學(xué)行為.最后從生物理論的角度出發(fā),分析了所得結(jié)果的生物意義,給出一些可行的系統(tǒng)控制策略與建議.第四章主要考慮了一類具有平方根功能反應(yīng)函數(shù)、捕食者之間相互干擾的脈沖三種群捕食—食餌模型.通過利用脈沖擾動技巧、弗洛凱理論、不等式理論、比較定理等基本理論,研究了該系統(tǒng)食餌滅絕周期解的存在性、全局漸近穩(wěn)定性的充分條件.通過構(gòu)建適當(dāng)?shù)腖yapunov函數(shù),采用比較的方法,進一步討論得到了系統(tǒng)持久的充分條件.最后通過數(shù)值模擬討論了干擾系數(shù)、脈沖周期等對系統(tǒng)穩(wěn)定性的影響,揭示了系統(tǒng)復(fù)雜的動力學(xué)性質(zhì).第五章主要從實際出發(fā),考慮到不同時刻有化學(xué)控制和生物控制、捕食者之間有相互干擾等因素對種群的實際影響,建立了一類脈沖三物種捕食-食餌模型.利用相關(guān)理論主要研究得到了食餌滅絕和系統(tǒng)持久的充分條件.然后舉例并進行數(shù)值模擬,進一步研究了系統(tǒng)的動力學(xué)性質(zhì).最后通過討論給出了所得結(jié)果的生物意義,結(jié)合相關(guān)控制策略給出了一些具體的意見與建議.總之,通過對上述系統(tǒng)的理論分析,得到了系統(tǒng)周期解的存在性、系統(tǒng)的穩(wěn)定性、系統(tǒng)的持久性等系列理論成果,所得結(jié)果推廣或改進了一些已有的理論結(jié)果,豐富了脈沖微分系統(tǒng)和生物動力系統(tǒng)理論.通過數(shù)值模擬,進一步研究了干擾因素、脈沖因素、功能反應(yīng)等對系統(tǒng)動力學(xué)性質(zhì)的廣泛影響,進一步揭示了系統(tǒng)復(fù)雜的動力學(xué)性質(zhì),為系統(tǒng)控制與生態(tài)平衡保護等給出了一些控制策略與建議.所得成果有較好的理論意義和一定的實際意義.
[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.
【學(xué)位授予單位】：桂林理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175

【參考文獻】

相關(guān)期刊論文 前3條

1 焦建軍;蔡紹洪;;脈沖捕獲捕食者與食餌具階段結(jié)構(gòu)的捕食-食餌模型[J];生物數(shù)學(xué)學(xué)報;2011年04期

2 王烈;陳斯養(yǎng);石茂;;帶有Beddington-DeAngelis功能反應(yīng)、脈沖、連續(xù)時滯和廣義擴散函數(shù)的捕食者-食餌系統(tǒng)的定性分析[J];工程數(shù)學(xué)學(xué)報;2011年03期

3 王育全;一類具Holling Ⅰ型功能反應(yīng)的食餌——捕食者模型的極限環(huán)及平衡點的全局穩(wěn)定性[J];懷化師專自然科學(xué)學(xué)報;1989年05期

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本文編號：2198259