Parametric pattern selection in a reaction-diffusion model
Pattern Formation and Solitons
2014-03-05 v1
Abstract
We compare spot patterns generated by Turing mechanisms with those generated by replication cascades, in a model one-dimensional reaction-diffusion system. We determine the stability region of spot solutions in parameter space as a function of a natural control parameter (feed-rate) where degenerate patterns with different numbers of spots coexist for a fixed feed-rate. While it is possible to generate identical patterns via both mechanisms, we show that replication cascades lead to a wider choice of pattern profiles that can be selected through a tuning of the feed-rate, exploiting hysteresis and directionality effects of the different pattern pathways.
Keywords
Cite
@article{arxiv.1310.2898,
title = {Parametric pattern selection in a reaction-diffusion model},
author = {Michael Stich and Gourab Ghoshal and Juan Pérez-Mercader},
journal= {arXiv preprint arXiv:1310.2898},
year = {2014}
}