Analysis of a mathematical model for the nest construction of social insects

2023 Fiscal Year Final Research Report

• Project/Area Number: 19K03594
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 12020:Mathematical analysis-related
• Research Institution: Kwansei Gakuin University
• Principal Investigator: Osaki Koichi 関西学院大学, 理学部, 教授 (40353320)
• Co-Investigator(Kenkyū-buntansha): 鳴海 孝之 山口大学, 大学院創成科学研究科, 准教授 (50599644) ; 陰山 真矢 岡山理科大学, 理学部, 講師 (80824060)
• Project Period (FY): 2019-04-01 – 2024-03-31
• Keywords: Deneubourg系 / Keller-Segel系 / 走化性 / 走性 / 時間大域解の存在 / パターン形成 / 反応拡散系 / ミツバチ

Outline of Final Research Achievements

We studied two mathematical models that describe the nesting processes of social insects, specifically termites and honeybees. These models are classified as three-component reaction-diffusion-advection systems. The advection in these models is particularly due to the taxis behavior of the insects, and the methods developed and refined by the principal investigator for two-component systems are effective for the mathematical analysis of such taxis systems. In this study, we identified new mathematical difficulties that arise in the three-component insect taxis systems. We advanced research on issues that include some of these difficulties, such as the global-in-time existence of solutions, the existence of finite-dimensional global attractors, the dynamics of solutions, and especially mode analysis in pattern formation of solutions.

Free Research Field

非線形解析学

Academic Significance and Societal Importance of the Research Achievements

本研究では社会性昆虫の営巣に関する数理モデルの基本的性質を明らかにしました．数理モデルの性質が明らかとなれば，その結果を現象の理解に役立てることができます．数理モデルを研究することの利点には，現象を予測し，さらに制御できる可能性が広がることなどがあります．本研究で扱った数理モデルは社会性昆虫の営巣に関する走性モデルですが，走性は昆虫のみならず白血球やがん細胞などにも存在しており，本研究を含む基礎研究が様々な自然現象の予測と制御へとつながる可能性があります．