Summary
International Symposium on Nonlinear Theory and its Applications
2009
Session Number:B2L-A
Session:
Number:B2L-A3
Spatially Periodic Pattern Formation in A Discrete Cell Based Model
Yue Ma, Hiroki Nagahara, Kenichi Yoshikawa,
pp.-
Publication Date:2009/10/18
Online ISSN:2188-5079
Summary:
Living organisms maintain their lives under far-from-equilibrium conditions by creating a rich variety of spatio-temporal structures in a self-organized manner, such as temporal rhythms, switching phenomena and development of the body. In this paper, we focus on the dynamical process of morphogens in somitogenesis in mice where propagation of the gene expression level plays an essential role in creating the spatially periodic patterns of the vertebral columns. We present a simple discrete reaction-diffusion model which includes neighboring interaction through an activator, but not diffusion of an inhibitor. We can produce stationary periodic patterns by introducing the effect of spatial discreteness to the field.