The Construction of a Mathematical Economic and GeographicalModel using the Complex System for an Economic Analysis of theUrban Formation Process and Its Computer Simulation

在人口流动的社会动力学模型的基础上，建立了经济地理数学模型。在本研究中，I.数学经济学家Takagi和M.以数值分析为专长的数学家田端从内生经济增长模型和数值分析的观点出发，对社会动力学模型进行了令人满意的分析。在人口移动的数学模型中，由于距离和时滞效应的特殊性，直接计算人口密度函数是困难的。因此，传统的数值分析方法无法应用于该问题的研究，这一课题的研究一直被推迟了很长一段时间。另一方面，随着数理统计计算理论的发展，利用种群密度函数的数理统计泛函数（容量和熵），提出了基于Agent的数学学校模型的评价算法。在计算中 关于我们 在经济地理数学模型中计算人口密度和地区真实的工资，采用了一个包含最高计算技术的数值分析程序包。因此，我们可以方便而准确地把握人口密度真实的工资的时空变化，并且即使我们让一个内生经济增长模型以各种形式联合，一个人口流动模型也可以通过这种方式快速地追赶模型的行为。我们考察了我们建立的原型模型与冯·图南模型、迪克西特-斯蒂格利茨模型、和Simon模型进行了数值实验。然后，我们考察了克鲁格曼提出的大城市是否通过自组织过程位于核心，以及在原型模型中是否可以解释边缘城市的形成过程，即多个卫星城市在郊区诞生，我们对所建立的原型模型进行了修正，并确定了最终的数学模型。通过最后的数学模型，我们能够解释城市的诞生，城市的许多层次结构的自组织，以及边缘城市的形成过程，即卫星城市围绕大都会诞生。少

Based on a population movement model of the socio-dynamics, we built a mathematical economic and geographical model. In this study, I. Takagi, a mathematical economist, and M. Tabata, a mathematician whose specialty is numerical analysis have satisfactorily analyzed the model of the socio-dynamics from the viewpoints of an endogenous economic growth model and numerical analysis.In a mathematical model of population movement, it is difficult to calculate a population density function directly due to specificity of the distance and time lag effects. Therefore, traditional methods in numerical analysis could not be applied to the study and the research on this topic has been delayed for a long time. On the other hand, by the advancement of the mathematical statistics theory of computation, by using mathematical statistical pan-function of the population density function (capacity and entropy), the algorithm to evaluate latromathematical school agent based model has been developed. In calc … More ulating population density and regional real wage in the mathematical economic and geographical model, a program package for numerical analysis incorporated the highest calculation technique was used. Therefore, we could grasp the spatial and temporal change of population density real wages easily and precisely, and a population movement model came to be able to in this way chase the behavior of the model quickly even if we let an endogenous economic growth model be alliance in various form.We inspected whether the prototype model that we built is consistent with such models as von Thunen model，Dixit-Stiglitz model，and Simon model by a numerical value experiment. Then, we examined whether a big city was located in the core by a self-organization process pointed out by Krugman and whether we could explain in the prototype model that a formationprocess of Edge City where plural satellite cities were born in the outskirts built.We repeated a correction of the prototype model that we built and decided the final mathematics model. By a final mathematical model, we were able to explain the birth of the city, self-organization of the many hierarchical structure of the city, and a formation process of Edge City where satellite cities were born around metropolis. Less