Global Bifurcation Analysis for tindorstruiding and Control of Pattern Dynan-dm

全局分岔分析及模式动态控制

• 批准号: 17540113
• 负责人: OGAWA Toshiyuki
• 金额: $ 2.35万
• 依托单位: Osaka University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2005
• 资助国家: 日本
• 起止时间: 2005 至 2007
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-17540113/
• 关键词: Wave Bifurcation; Degenerate Hoof Bifurcation; Bifurcation Analysis; Electro-Chemical Oscillation; 3-component Reaction-Diffusion system; Turing Bifuracation; Pattern Selection; 標準形; Rotating Wave; Standing Wave; 反応拡散系

Oscillatory Reaction-Diffusion systems are studied from the point of bifurcation analysis to understand the various types of spatio-temporal patterns observed in a certain electro-chemical oscillation. It turned out, first, that a nontrivial oscillatory mode becomes observable by virtue of a global negative inhibition. Second, we see that the mode interactions between ±1 modes determine the pattern selection of rotating and standing waves. Moreover, by this bifurcation analysis we can easily control the result of experiments. We also find that this model can be considered as a special case of 3-component reaction-diffusion system which also exhibits so-called wave bifurcation. Mode interaction between Turing and Wave bifurcation is also studied.

振荡反应扩散系统从分岔分析的角度进行研究，以了解在某种电化学振荡中观察到的各种类型的时空模式。事实证明，首先，通过全局可以观察到非平凡的振荡模式。其次，我们发现±1模式之间的模式相互作用决定了旋转波和驻波的模式选择。此外，通过这种分岔分析，我们还可以轻松控制实验结果。发现该模型可以被视为三分量反应扩散系统的特例，该系统也表现出所谓的波分岔，并且还研究了图灵和波分岔之间的模式相互作用。

项目成果

Degenerate Hopf Instability in Oscillatory Reaction-Diffusion Equations

振荡反应扩散方程中的简并Hopf不稳定性

• 发表时间: 2007
• 作者: T. Ogawa

Rayleigh-Benard convection in a rectangular domain

矩形域中的瑞利-贝纳德对流

• 发表时间: 2006
• 作者: T.; Ogawa; et. al.
• 通讯作者: et. al.

Krein's formula for indefinite multipliers in linear periodic Hamiltonian systems

线性周期哈密顿系统中不定乘数的 Krein 公式

• 发表时间: 2006
• 作者: Masataka Kuwamura; et al.
• 通讯作者: et al.

Degenerate Hopf instability in RD systems with global inhibition

具有全局抑制的 RD 系统中的简并 Hopf 不稳定性

• 发表时间: 2005
• 作者: Toshi; OGAWA
• 通讯作者: OGAWA

Bifurcation analysis to Swift-Hohenberg equation with perturbed boundary conditions

扰动边界条件下 Swift-Hohenberg 方程的分岔分析

• 发表时间: 2007
• 作者: T.; Ogawa; et. al.
• 通讯作者: et. al.