New theory for transient dynamics in reaction-diffusion systems allowing collapse of attractors

2014 Fiscal Year Final Research Report

• Project/Area Number: 24654044
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Global analysis
• Research Institution: Ryukoku University
• Principal Investigator: MORITA YOSHIHISA 龍谷大学, 理工学部, 教授 (10192783)
• Co-Investigator(Kenkyū-buntansha): SUZUKI Kanako 茨城大学, 理学部, 准教授 (10451519) ; KUWAMURA Masataka 神戸大学, 人間発達環境学研究科, 教授 (30270333)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 遷移ダイナミクス / 反応拡散系 / 大域アトラクタ / アトラクタの崩壊 / 散逸力学系 / 保存則 / 摂動系 / チューリング的パターン

Outline of Final Research Achievements

We consider reaction-diffusion systems having a global attractor which collapses and turns to be a single stationary state by a perturbation. Although the dynamical structure largely changed by the perturbation, there is a perturbed orbit close to the unperturbed one during a transient time.　In a specific reaction-diffusion system with conservation law we　show for the perturbed system that a Turing-like wave takes place and it changes to a single spike, then the pattern finally collapses. The perturbed system has no longer steady state solutions which induce a Turing type instability. Nonetheless in the transient dynamics such a Turing-like pattern can be shown.

Free Research Field

応用解析