Mathematical mechanism for periodic structure formation of somitogenesis

体节发生周期结构形成的数学机制

• 批准号: 20740224
• 负责人: TERAMOTO Takashi
• 金额: $ 2.33万
• 依托单位: Chitose Institute of Science and Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20740224/
• 关键词: 反応拡散系; 数値解析; 生物物理; 応用数学; 非線形科学; 分岐理論; スポットダイナミクス; 非線形物理

Heterogeneity is one of the most important and ubiquitous types of external perturbations with respect to pulse propagation in biological signal processing. To know the behaviors of pulse waves in such media is closely related to studying the collision process between the pulse and the heterogeneity-induced-ordered pattern. The reduced dynamics near a singularity is able to capture the rotational spot motion in the full partial differential equations by ordinary differential equations. We also study a spontaneous pulse generating mechanism caused by the heterogeneity of jump type. Exploring the global bifurcation structure of PGs as periodic solutions, we find firstly the conditions under which they emerge, i.e., the onset of pulse generators, secondly a candidate for the organizing center producing their variety.

非均质性是生物信号处理中脉冲传播过程中最重要、最普遍的外部扰动之一。了解脉冲波在这种介质中的行为，与研究脉冲与非均质有序图样的碰撞过程密切相关。在奇异点附近的简化动力学可以用常微分方程来捕捉全偏微分方程中的旋转点运动。我们还研究了由跳型非均质性引起的自发脉冲产生机制。我们以周期解的形式探讨了PGs的全局分岔结构，首先找到了它们出现的条件，即脉冲发生器的起始点，其次找到了产生它们变化的组织中心的候选点。

项目成果

A nested sequence of transitions for collision dynamics in dissipative systems

耗散系统中碰撞动力学的嵌套过渡序列

• 发表时间: 2008
• 期刊: BULLETIN of the Institute of Mathematics Academia Sinica New Series 3(4)
• 作者: M. Efendiev;E. Nakaguchi and K. Osaki;Masaaki Yadome
• 通讯作者: Masaaki Yadome

Morphological characterization of the diblock copolymer problem

二嵌段共聚物问题的形态表征

• 发表时间: 2010
• 期刊: Japan Journal of Industrial and Applied Mathematics
• 影响因子: 0.9
• 作者: T.Teramoto;Y.Nishiura
• 通讯作者: Y.Nishiura

Dynamics of traveling spots in heterogeneous media

异构介质中行进点的动力学

• 发表时间: 2010
• 作者: 須永知夏;峰真如;三竿和也;山中由也;T.Teramoto
• 通讯作者: T.Teramoto

Spot Dynamics of Reaction-Diffusion Systems in Heterogeneous Media

异质介质中反应扩散系统的点动力学

• 发表时间: 2009
• 作者: X. Yuan;T. Termaoto;Y. Nishiura
• 通讯作者: Y. Nishiura

砂漠化問題のバスタブモデル

荒漠化问题的浴缸模型

• 发表时间: 2010
• 期刊: 数理科学
• 作者: 西浦廉政;寺本敬
• 通讯作者: 寺本敬