Pattern formation driven by cross--diffusion in a 2D domain
Pattern Formation and Solitons
2014-03-03 v1 Mathematical Physics
Dynamical Systems
math.MP
Abstract
In this work we investigate the process of pattern formation in a two dimensional domain for a reaction-diffusion system with nonlinear diffusion terms and the competitive Lotka-Volterra kinetics. The linear stability analysis shows that cross-diffusion, through Turing bifurcation, is the key mechanism for the formation of spatial patterns. We show that the bifurcation can be regular, degenerate non-resonant and resonant. We use multiple scales expansions to derive the amplitude equations appropriate for each case and show that the system supports patterns like rolls, squares, mixed-mode patterns, supersquares, hexagonal patterns.
Cite
@article{arxiv.1211.4412,
title = {Pattern formation driven by cross--diffusion in a 2D domain},
author = {G. Gambino and M. C. Lombardo and M. Sammartino},
journal= {arXiv preprint arXiv:1211.4412},
year = {2014}
}