Boundary-Induced Pattern Formation from Temporal Oscillation: Spatial Map Analysis
Pattern Formation and Solitons
2017-02-01 v1
Abstract
Boundary-induced pattern formation from a spatially uniform state is investigated using one-dimensional reaction-diffusion equations. The temporal oscillation is successively transformed into a spatially periodic pattern, triggered by diffusion from the fixed boundary. We introduced a spatial map, whose temporal sequence, under selection criteria from multiple stationary solutions, can completely reproduce the emergent pattern, by replacing the time with space. The relationship of the pattern wavelength with the period of oscillation is also obtained. The generality of the pattern selection process and algorithm is discussed with possible relevance to biological morphogenesis.
Cite
@article{arxiv.1603.01038,
title = {Boundary-Induced Pattern Formation from Temporal Oscillation: Spatial Map Analysis},
author = {Takahiro Kohsokabe and Kunihiko Kaneko},
journal= {arXiv preprint arXiv:1603.01038},
year = {2017}
}
Comments
17pages