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

基于社会动力学的人口流动模型，我们建立了数学经济和地理模型。在本研究中，数理经济学家I. Takagi和专门从事数值分析的数学家M. Tabata从内生经济增长模型和数值分析的角度对社会动力学模型进行了令人满意的分析。在人口流动的数学模型中，由于距离和时滞效应的特殊性，很难直接计算人口密度函数。因此，传统的数值分析方法无法应用于该研究，该课题的研究被拖延了很长时间。另一方面，随着数理统计计算理论的进步，利用人口密度函数的数理统计泛函数（容量和熵），发展了基于数学学派代理模型的评估算法。在数学经济和地理模型中计算人口密度和地区实际工资时，使用了包含最高计算技术的数值分析程序包。因此，我们可以轻松准确地掌握人口密度实际工资的时空变化，这样，即使让内生经济增长模型以各种形式联盟，人口流动模型也能快速追随模型的行为。通过数值实验检验我们建立的原型模型与von Thunen模型、Dixit-Stiglitz模型、Simon模型等模型是否一致。然后，我们检验了克鲁格曼指出的自组织过程是否会导致大城市位于核心，以及是否可以在原型模型中解释在郊区诞生多个卫星城市的边缘城市的形成过程。我们对所建立的原型模型进行了重复修正，并确定了最终的数学模型。通过最终的数学模型，我们能够解释城市的诞生、城市众多层级结构的自组织，以及围绕大都市诞生卫星城市的边缘城市的形成过程。较少的

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