资源型产业可持续发展的离散动力学模型分析

发布时间：2018-03-05 12:37

  本文选题：资源型产业　切入点：flip分叉　出处：《中南民族大学》2015年硕士论文　论文类型：学位论文

【摘要】：本文在陈明义等人提出的资源-经济可持续发展的最优模型的动态方程的基础上,首先假定资源开发速度μ保持不变,构造了可再生资源存量与产量之间相互作用的一维离散动力学模型,讨论资源型产业的产量对资源可持续利用的影响;其次当政府对资源开发速度μ实施动态管理时,建立了可再生资源存量及资源开发速度的二维离散动力学模型,研究了在控制资源开发速度下,资源型产业的产量对资源可持续利用的影响。首先,我们简单介绍了可再生资源型产业可持续发展的研究背景及意义,并阐述了本论文的研究内容、研究方法和内容安排,从整体上对本论文有一个认识。其次,针对一维模型,我们运用数学分析的方法分析了一维系统的正不动点的存在性条件,以及一维系统的正不动点的局部稳定性,得出相关定理,接着通过数值模拟验证了定理的准确性,最后对系统进行全局分析,研究了随着产量的变化,系统的可行吸引域结构的变化情况,并绘制出可行吸引域图;针对二维模型,我们同理分析了系统的正不动点的存在性和局部稳定性,特别的,运用中心流形定理及规范型理论研究了二维系统在flip分叉处和Neimark-Sacker分叉处正不动点的稳定性,得出相关定理,接着通过运用Matlab、IDMC进行数值模拟验证了定理的准确性,并绘制出一维系统的李雅谱诺夫指数谱图,以及资源存量随时间演变的时间序列图,证明了二维系统可以控制一维系统的混沌行为,然后运用吸引域的全局分叉理论分析了二维系统的全局动力学行为,研究可行吸引域随企业产量的变化而发生的结构和大小变化,最后运用拓扑马蹄理论研究了二维系统的混沌行为,根据李清都、杨晓松教授提出的拓扑马蹄的相关理论,借助Matlab工具箱中的HsTool工具,当取参数固定时,在混沌吸引子中找到了一个拓扑马蹄证明了系统是超混沌的。最后,从模型出发,有针对性的提出对应措施,并特别指出,如果政府对资源开发速度实行动态配额管理控制资源的消耗,不但能保持一定的资源存量,使人们长久的获取资源,还可以满足可再生资源型产业对较高产量的要求。
[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.
【学位授予单位】：中南民族大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O175
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本文编号：1570261