本文選題：資源型產業(yè)　切入點：flip分叉　出處：《中南民族大學》2015年碩士論文　論文類型：學位論文

【摘要】：本文在陳明義等人提出的資源-經濟可持續(xù)發(fā)展的最優(yōu)模型的動態(tài)方程的基礎上,首先假定資源開發(fā)速度μ保持不變,構造了可再生資源存量與產量之間相互作用的一維離散動力學模型,討論資源型產業(yè)的產量對資源可持續(xù)利用的影響;其次當政府對資源開發(fā)速度μ實施動態(tài)管理時,建立了可再生資源存量及資源開發(fā)速度的二維離散動力學模型,研究了在控制資源開發(fā)速度下,資源型產業(yè)的產量對資源可持續(xù)利用的影響。首先,我們簡單介紹了可再生資源型產業(yè)可持續(xù)發(fā)展的研究背景及意義,并闡述了本論文的研究內容、研究方法和內容安排,從整體上對本論文有一個認識。其次,針對一維模型,我們運用數(shù)學分析的方法分析了一維系統(tǒng)的正不動點的存在性條件,以及一維系統(tǒng)的正不動點的局部穩(wěn)定性,得出相關定理,接著通過數(shù)值模擬驗證了定理的準確性,最后對系統(tǒng)進行全局分析,研究了隨著產量的變化,系統(tǒng)的可行吸引域結構的變化情況,并繪制出可行吸引域圖;針對二維模型,我們同理分析了系統(tǒng)的正不動點的存在性和局部穩(wěn)定性,特別的,運用中心流形定理及規(guī)范型理論研究了二維系統(tǒng)在flip分叉處和Neimark-Sacker分叉處正不動點的穩(wěn)定性,得出相關定理,接著通過運用Matlab、IDMC進行數(shù)值模擬驗證了定理的準確性,并繪制出一維系統(tǒng)的李雅譜諾夫指數(shù)譜圖,以及資源存量隨時間演變的時間序列圖,證明了二維系統(tǒng)可以控制一維系統(tǒng)的混沌行為,然后運用吸引域的全局分叉理論分析了二維系統(tǒng)的全局動力學行為,研究可行吸引域隨企業(yè)產量的變化而發(fā)生的結構和大小變化,最后運用拓撲馬蹄理論研究了二維系統(tǒng)的混沌行為,根據李清都、楊曉松教授提出的拓撲馬蹄的相關理論,借助Matlab工具箱中的HsTool工具,當取參數(shù)固定時,在混沌吸引子中找到了一個拓撲馬蹄證明了系統(tǒng)是超混沌的。最后,從模型出發(fā),有針對性的提出對應措施,并特別指出,如果政府對資源開發(fā)速度實行動態(tài)配額管理控制資源的消耗,不但能保持一定的資源存量,使人們長久的獲取資源,還可以滿足可再生資源型產業(yè)對較高產量的要求。
[Abstract]:On the basis of the dynamic equation of the optimal model of resource-economy sustainable development proposed by Chen Mingyi et al, this paper first assumes that the speed of resource development 渭 remains unchanged. In this paper, a one-dimensional discrete dynamic model of the interaction between renewable resource stock and output is constructed to discuss the effect of the output of resource-based industry on the sustainable utilization of resources. Secondly, when the government implements the dynamic management of the resource development speed 渭, In this paper, a two-dimensional discrete dynamic model of renewable resource stock and resource development speed is established, and the effect of the output of resource-based industry on the sustainable utilization of resources is studied under the control of resource development speed. This paper briefly introduces the research background and significance of sustainable development of renewable resource industry, and expounds the research content, research methods and content arrangement of this paper. The existence condition of positive fixed point and the local stability of positive fixed point of one-dimensional system are analyzed by means of mathematical analysis, and the relevant theorems are obtained, and the accuracy of the theorem is verified by numerical simulation. Finally, the global analysis of the system is carried out, and the change of the structure of the feasible region of attraction of the system with the change of yield is studied, and the map of the feasible region of attraction is drawn. In this paper, we analyze the existence and local stability of positive fixed points of the system. In particular, by using the center manifold theorem and the normal form theory, we study the stability of the positive fixed points at the flip bifurcation and the Neimark-Sacker bifurcation for two-dimensional systems, and obtain the relevant theorems. Then the accuracy of the theorem is verified by numerical simulation with Matlab IDMC, and the Lyapunov exponent spectrum of one-dimensional system and the time series diagram of resource stock evolution with time are drawn. It is proved that the two-dimensional system can control the chaotic behavior of the one-dimensional system, and then the global dynamical behavior of the two-dimensional system is analyzed by using the global bifurcation theory in the domain of attraction. This paper studies the structure and size change of feasible attraction region with the change of enterprise output. Finally, the chaotic behavior of two-dimensional system is studied by using topological horseshoe theory. According to the relevant theory of topological horseshoe proposed by Li Qing and Professor Yang Xiaosong, With the help of the HsTool tool in the Matlab toolbox, when the parameters are fixed, a topological horseshoe is found in the chaotic attractor to prove that the system is hyperchaotic. If the government implements dynamic quota management to control the consumption of resources, it can not only maintain a certain amount of resources, make people obtain resources for a long time, but also meet the requirements of renewable resource industry for higher output.
【學位授予單位】：中南民族大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：O175
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本文編號：1570261