Mathematical mechanism for periodic structure formation of somitogenesis

在生物信号处理中，异质性是影响脉冲传播的最重要和最普遍的外部扰动类型之一。了解脉冲波在这类介质中的行为与研究脉冲波与非均匀性诱导有序斑图的碰撞过程密切相关。奇点附近的约化动力学能够通过常微分方程在全偏微分方程中捕获旋转光斑运动。我们还研究了跳跃型不均匀性引起的自发脉冲产生机制。研究了PG作为周期解的全局分支结构，首先得到了它们出现的条件，即，脉冲发生器的开始，其次是候选人的组织中心生产他们的品种。

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.