Simultaneous occurrence of explosion and extinction in spatial evolutionary game for rapid movement of population

2023 Fiscal Year Final Research Report

• Project/Area Number: 19K03641
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 12040:Applied mathematics and statistics-related
• Research Institution: Osaka Metropolitan University (2022-2023); Osaka Prefecture University (2019-2021)
• Principal Investigator: TABATA Minoru 大阪公立大学, 大学院理学研究科, 客員研究員 (70207215)
• Project Period (FY): 2019-04-01 – 2024-03-31
• Keywords: 空間進化ゲーム / 人口移動

Outline of Final Research Achievements

The main objective of this study was to prove, by a combination of mathematical statistical and numerical methods, the expected proposition derived from numerical experiments: 'Rapid population outflows and inflows in a singly connected area cause the population to disappear in one subregion, while the population distribution in another subregion converges to a delta function in the superfunctional sense'. The proposition was successfully proved, albeit with restrictions on the parameter values. The starting point was Villani's work (application of the statistical method of entropy to the Boltzmann equation, a non-linear partial differential and integral equation of statistical mechanics). The results were applied to precise numerical calculations of population movements. The statistics of the industrial and agricultural wage distributions were calculated using this method.

Free Research Field

応用数学

Academic Significance and Societal Importance of the Research Achievements

日本では少子高齢化に伴って，地域間の人口移動は緩やかになると，かつては信じられていた．しかし長期に渡る過疎化によって人口減少が続いている地方では，集落が短期間に消滅するような人口流出が起き，それと同時に東京のような大都市では，急激な人口の流入が起きることが確実視されている．このように都市の人口爆発と地方の人口消滅は，人口爆発する都市を多く抱える中国や東南アジアは勿論，日本にとっても重要政策課題の一つである．本研究は，このようなアジアの重要政策課題に対して数理解析的アプローチを試みるものであり，大きな社会的意義を有していると言える．