Localized structures on reaction-diffusion networks

2022 Fiscal Year Final Research Report

• Project/Area Number: 19K20357
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 61040:Soft computing-related
• Research Institution: Kagoshima University
• Principal Investigator: Shigefumi Hata 鹿児島大学, 理工学域理学系, 准教授 (70735927)
• Project Period (FY): 2019-04-01 – 2023-03-31
• Keywords: パターン形成 / 複雑ネットワーク

Outline of Final Research Achievements

We analyzed the mechanism of the species localization in reaction-diffusion networks. We proved analytically that uniform distribution of species becomes unstable when a model parameter exceeds a certain threshold. Numerical results suggest that stationary particle-like structures (spots) develop spontaneously after the instability. We also found numerically that the stationary spot becomes unstable after another instability, which leads the onset of translational motion of the spot. After this instability, the spot moves over the entire network.

Free Research Field

非線形動力学

Academic Significance and Societal Importance of the Research Achievements

局在構造を形成する反応拡散モデルはこれまで主に連続媒質上で解析が行われ，局在構造の形成メカニズムの理解が進められてきた．一方，複雑ネットワーク上に局在構造を形成するモデルはこれまでに提案されておらず，ネットワーク上で物質の局在化が起こるメカニズムは明らかになっていない．本研究では従来とは異なる機構によりネットワーク上で局在化が起こり得ることを示した．これは基礎的な結果であるが，我々の身の回りで起こる物質の局在化現象を理解する上で重要な知見である．