Mathematical mechanism for periodic structure formation of somitogenesis

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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.