Mathematical mechanism for periodic structure formation of somitogenesis

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。

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.