一类分数阶IS-LM宏观经济模型及其复杂性研究

发布时间：2018-01-02 12:43

本文关键词：一类分数阶IS-LM宏观经济模型及其复杂性研究　出处：《天津大学》2015年博士论文　论文类型：学位论文

【摘要】：在目前经济社会的“新常态”大背景下,我国宏观经济正经历着空前的发展转型和巨大的历史机遇,随着我国经济环境的进一步放开,利率市场化的逐步拓展,我国宏观经济所面对的问题和机遇也逐步发生着变化。在此基础上,本文梳理了我国宏观经济的发展状况,根据混沌理论和分岔理论介绍了相应的三维和四维非线性IS-LM经济模型,对宏观经济的运行状态进行模拟。进而通过分数阶理论对非线性IS-LM经济模型进行改进,保证经济变量的“记忆特性”,探究了分数阶宏观经济系统的运行状态和复杂动力学特征。得到了如下结论:1.本文给出了相应的非线性IS-LM动态演化模型,并且描述了该模型在发生“流动性陷阱”时的特定参数条件。在分析非线性IS-LM模型的内在复杂性过程中,研究了系统的均衡点、稳定性、Hopf分岔等复杂动力学特征。在对Hopf分岔进行深入分析的过程中,创新性地引入第一Lyapunov系数的概念,对Hopf分岔所产生的极限环的稳定性进行了研究,给出了当Hopf分岔所产生的极限环处于稳定状态时,系统的参数取值范围。2.创新性地通过分数阶理论,构建了三维和四维分数阶IS-LM宏观经济模型,研究分析了分数阶系统的解的稳定性和复杂动力学特征。着重分析了分数阶系统的Hopf分岔状态,表明分数阶系统可以通过改变系统阶数,来实现Hopf分岔,从而不影响相关的经济变量。具有很好的实际应用前景。3.深入分析了系统阶数对分数阶IS-LM模型的运行状态的影响,通过系统所有维度阶数同时变化和单一维度阶数变化两个角度,分析阶数对系统状态的影响。分析表明,系统阶数的变化会对运行状态产生相似的影响,通过对系统阶数的调整,保障在整数阶条件下处于混沌状态的系统进入稳定收敛状态。4.创新性地分析了参数变化对分数阶与整数阶系统的影响,研究表明参数变化可以使得整数阶条件下处于混沌状态的系统,在分数阶条件下能够实现较大范围的收敛。或者改变了当系统收敛时经济参数的取值范围。本文的研究说明了分数阶理论在经济管理领域具有很好的分析能力和应用前景,分数阶经济系统可以通过改变系统的阶数,在保证重要经济参数不变的前提下,实现宏观经济的稳定收敛。因此本文的结论为国家开展“新常态”下的宏观经济调控,保障宏观经济整体健康稳定有序运行,提供了一种可行的调控思路和方法。
[Abstract]:In the current economic society's "new normal" under the background of China's macro economy is experiencing unprecedented development and transformation of great historical opportunity, with the further opening of China's economic environment, and gradually expand the market interest rates, China's macroeconomic problems and opportunities are gradually changing. On the basis of in this paper, reviews the development situation of China's macro economy, according to the theory of chaos and bifurcation theory and introduces the corresponding 3D and 4D nonlinear IS-LM economic model, the running state of macroeconomic simulation. Then through the modification of the IS-LM nonlinear economic model of fractional order theory, ensure economic variables "memory effect", explores the the running state of the fractional macroeconomic system and complex dynamics. Obtained the following conclusions: 1. this paper gives the corresponding IS-LM nonlinear dynamic evolution model, and description The model in the "specific parameters of the liquidity trap". In the process of the inherent complexity of nonlinear analysis of IS-LM model, the stability of equilibrium points, Hopf bifurcation system, the complex dynamic characteristics. In the process of in-depth analysis of the Hopf bifurcation of the concept, the introduction of innovative first Lyapunov coefficients and the stability of limit cycle generated by the Hopf bifurcation of limit is given when the Hopf bifurcation generated by the ring is in a steady state, the range of parameter values.2. through new fractional order theory system, construct the three-dimensional and four-dimensional fractional IS-LM macroeconomic model, analyzed the stability of solutions of fractional order system and complex dynamic characteristics are analyzed. The Hopf bifurcation condition of fractional order system, show that the fractional order system can change the order of the system, to achieve the Hopf bifurcation, which is not The influence of the related economic variables. The prospects for practical application of.3. good in-depth analysis of the impact of system order of fractional IS-LM model running state, through two aspects of all dimensions of order at the same time change and single dimension order changes, analysis of the impact of the order of the system state. The analysis shows that the change of system order the number will have a similar influence on the running state, according to the order of system adjustment, security system is in a chaotic state in the integer order conditions into a stable convergence state.4. innovatively analyzes the influence of parameter variation on the fractional and integer order system, research shows that the parameter changes can be in chaotic state makes the integer order conditions, to achieve a wide range of convergence in the fractional conditions. The range or change when the system parameters of the economic convergence. This study shows that the fractional order The theory has the analysis ability and good application prospect in the field of economic management, economic system can be obtained by fractional order change system, under the premise of ensuring the same important economic parameters, to achieve stable macroeconomic convergence. The conclusion of this paper therefore carry out macroeconomic regulation under the new normal for the country, security and orderly operation the overall stability of macroeconomic health, provides a feasible control ideas and methods.

【学位授予单位】：天津大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：F124

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