Mathematical Economic Model of the Complex System in International Economics

在属于被称为复杂系统经济学和经济物理学的复杂系统科学的数学社会科学领域中，通过使用统计力学技术来建立许多数学模型以分析社会经济现象。然而，在复杂系统科学这一新的领域中，与统计力学理论同等的数学基础几乎还不存在。为此，我们用泛函分析的方法对一个数学经济模型进行了分析。我们建立了一个数学模型，表达了一种自组织现象，这种自组织现象是由劳动力流动和经济增长的相互作用引起的，就像欧盟市场一体化一样。在统计力学中，人口运动理论中的主方程的解被证明非常接近于福克-普朗克方程的解，这是通过使用物理学允许的程度的接近性中的Kramers-Moyal展开来实现的，当所需的运动成本为 ...更多信息 国际劳动力流动的空间足够大。此外，我们能够在数学上和精确地证明霍特林的人口运动理论与魏德利希-哈格的人口运动理论的一致性。在一篇题为“人口迁移与生物粒子扩散之间的几何相似性”的文章中，我们制造了一个特工一种描述人口流动现象的基于模型，当表示某种地方经济优势的效用函数是线性函数或代理密度的二次函数。此外，在传统的研究中，Kramers-Moyal展开和高次项展开的收敛性的数学精确证明是非常困难的，因此几乎没有提供有意义的结果。然而，我们证明了，当人口迁移的代价足够大时，用我们修正的有限Kramers-Moyal展开式求解人口迁移理论中的主方程与求解Fokker-Planck方程非常接近。少

In a field of mathematical social science that belongs to a science of the complex system to be called economics of complex system and economic physics, many mathematical models are built by using technique of statistical mechanics for analysis of a social economic phenomenon. However, in a new field of a science of the complex system, a mathematical foundation equal to that for the theory of statistical mechanics does not almost exist yet. Therefore, we analyzed a mathematical economic model with a method of functional analysis. We built a mathematical model that expresses a self-organization phenomenon that caused by interaction of labor movement and economic growth like that happened in the EU market unification. In statistical mechanics a solution of a master equation in a population movement theory proved to be very close to a solution of the Fokker-Planck equation by using the Kramers-Moyal expansion in closeness of degree permitted in physics when the moving cost that is necessa … More ry for international labor mobility is large enough. In addition, we were able to prove mathematically and precisely the consistency of the theory of population movement of Hotelling's with that of Weidlich-Haag's.In an article, "A geometrical similarity between migration of human population and diffusion of biological particles", we built an Agent-based Model that describes a population movement phenomenon when a utility function expressing a certain local economic advantage is a linear function or a quadratic function of agent density. Furthermore, in conventional studies, mathematically precise proofs for the convergence of the Kramers-Moyal expansion and an expansion of high degree terms were extremely difficult, so an almost meaningful result was not provided. However, we proved that a solution for a master equation in a theory of population movement by using the limited Kramers-Moyal expansion that modified by us was very close to a solution for the Fokker-Planck equation when the cost of population movement was large enough. Less