本文選題：外來物種入侵　切入點：生物經(jīng)濟(jì)系統(tǒng)　出處：《沈陽工業(yè)大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：生物數(shù)學(xué)是應(yīng)用數(shù)學(xué)思維,嘗試從數(shù)學(xué)的角度研究和解決生物學(xué)上的問題,外來物種入侵常常損害本地的生態(tài)系統(tǒng)和地理構(gòu)造,給生產(chǎn)生活造成了不良影響。用生物數(shù)學(xué)來研究外來物種入侵下的生態(tài)系統(tǒng),了解經(jīng)濟(jì)生產(chǎn)和種群的動態(tài)學(xué)行為,對人類社會的穩(wěn)定和發(fā)展能起到一定的積極作用。本文以外來物種入侵為背景,介紹了三種不同生物關(guān)系下的生態(tài)系統(tǒng),包括捕食關(guān)系、抑制關(guān)系和競爭關(guān)系,三種生態(tài)系統(tǒng)都考慮了種群分階段結(jié)構(gòu)的情況。首先,根據(jù)外來物種與原生態(tài)系統(tǒng)中的物種存在的捕食關(guān)系,對分階段結(jié)構(gòu)的帶功能反應(yīng)函數(shù)的生態(tài)系統(tǒng)做永久性分析;其次,根據(jù)廣義生物經(jīng)濟(jì)理論和考慮入侵的物種釋放化學(xué)物質(zhì)影響本地物種且本地物種出現(xiàn)時滯變化的情況,進(jìn)行了分階段結(jié)構(gòu)的時滯生物模型的Hopf分岔、平衡點周期性分析;最后,考慮外來物種與本地物種存在競爭關(guān)系,進(jìn)行了加入特定擾動項后的生物經(jīng)濟(jì)系統(tǒng)的H?保性能控制分析。具體研究工作如下:(1)介紹了本文的研究背景,其中包括現(xiàn)如今外來物種的入侵情況、原因及影響,先著重分析了外來物種入侵下的魚類種群生存和捕撈情況;其次介紹了生物控制分析方法,包括分階段結(jié)構(gòu)的Holling IV系統(tǒng)的分析、時滯系統(tǒng)的Hopf分岔分析、生物系統(tǒng)的保性能控制分析;然后,簡述了外來物種和廣義生物系統(tǒng)的研究進(jìn)展;最后,介紹了本文的主體內(nèi)容。(2)研究了外來物種入侵下的具捕食關(guān)系的一種帶有Holling IV的分階段結(jié)構(gòu)的非自治捕食系統(tǒng),基于兩種基礎(chǔ)增長模型,得到生物捕食模型。然后通過分析驗證,得出一組使系統(tǒng)永久性存在的充分條件,即滿足該條件的情況下,可達(dá)到生態(tài)系統(tǒng)中所涉及物種的長久共存的狀態(tài),通過仿真例子給出說明。(3)研究了外來物種入侵下的具抑制關(guān)系的一種時滯分階段結(jié)構(gòu)的生物經(jīng)濟(jì)系統(tǒng)。本文使用適當(dāng)?shù)膮?shù)化和線性化方法,運(yùn)用中心流形和龐加萊標(biāo)準(zhǔn)型辦法,分析了時滯廣義系統(tǒng)Hopf分岔的方向、穩(wěn)定性及周期性,仿真算例驗證了所得結(jié)論的正確性。(4)研究了外來物種入侵下的具競爭關(guān)系的一種分階段結(jié)構(gòu)的廣義生物經(jīng)濟(jì)系統(tǒng)的保性能控制問題。從人工捕獲收益、對外來物種的凈化能力入手,建立廣義系統(tǒng)模型,討論平衡點附近的性質(zhì),然后通過T-S模糊方法建立廣義線性生物模型,在此基礎(chǔ)上添加受自然因素影響的滿足Lipschitz條件的擾動項,確定性能指標(biāo),用LMI方法給出簡化的不確定廣義系統(tǒng)保性能控制器存在的充分條件,仿真數(shù)例驗證了研究結(jié)果的有效性。
[Abstract]:Biological mathematics is applied mathematical thinking, trying to solve the biological problems from the mathematical perspective, alien species invasion often damage the local ecosystem and geographical structure, The biological mathematics is used to study the ecosystem of alien species invasion, to understand the economic production and the dynamic behavior of the population, This paper, based on the invasion of alien species, introduces the ecosystem of three different biological relationships, including predator relationship, inhibition relationship and competition relationship, which can play a positive role in the stability and development of human society. First, according to the predator-prey relationship between alien species and species in the original ecosystem, a permanent analysis of the ecosystem with functional response function is carried out on the basis of the predator-prey relationship between alien species and species in the original ecosystem. Based on the generalized bio-economic theory and the situation that the invasive species release chemical substances to affect the local species and the local species show time-delay variation, the Hopf bifurcation and equilibrium periodic analysis of the time-delay biological model with a phased structure are carried out. Finally, the periodic analysis of the equilibrium point is given. Considering the competitive relationship between alien species and native species, the H? Analysis of guaranteed cost control. The specific research work is as follows: (1) introduce the research background of this paper, including the invasion of alien species nowadays, the reasons and effects, and analyze the survival and fishing situation of the fish population under the invasion of alien species. Secondly, the biological control analysis methods are introduced, including the analysis of the Holling IV system with phased structure, the Hopf bifurcation analysis of the time-delay system, the guaranteed cost control analysis of the biological system, and the research progress of the alien species and the generalized biological system. Finally, this paper introduces the main content of this paper. (2) A non-autonomous predator-prey system with a phased structure of Holling IV is studied under the invasion of alien species, based on two basic growth models. The biological predator model is obtained. Then, by analysis and verification, a set of sufficient conditions for the permanent existence of the system are obtained, that is, if the condition is satisfied, the species involved in the ecosystem can coexist for a long time. A simulation example is given to illustrate how to study a time-delay, phased structure bio-economic system with suppression relationship under alien species invasion. In this paper, appropriate parameterization and linearization methods are used. The direction, stability and periodicity of Hopf bifurcation for singular systems with time delay are analyzed by means of the central manifold and the Poincare canonical form method. A simulation example is given to verify the correctness of the conclusions obtained. (4) the guaranteed cost control problem of a phased structure of generalized bio-economy system with competitive relationship under invasive alien species is studied. Based on the purification ability of alien species, the generalized system model is established, and the properties near the equilibrium point are discussed. Then the generalized linear biological model is established by T-S fuzzy method. On this basis, the perturbation terms which satisfy the Lipschitz condition are added, and the performance index is determined. By using the LMI method, the sufficient conditions for the existence of guaranteed cost controllers for uncertain singular systems are given. Several examples are given to verify the validity of the results.
【學(xué)位授予單位】：沈陽工業(yè)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175

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