Bistable reaction-diffusion on a network
Adaptation and Self-Organizing Systems
2015-06-22 v1
Abstract
We study analytically and numerically a bistable reaction-diffusion equation on an arbitrary finite network. We prove that stable fixed points (multi-fronts) exist for any configuration as long as the diffusion is small. We also study fold bifurcations leading to depinning and give a simple depinning criterion. These results are confirmed by using continuation techniques from bifurcation theory and by solving the time dependent problem near the treshold. A qualitative comparison principle is proved and verified for time dependent solutions, and for some related models.
Cite
@article{arxiv.1406.7742,
title = {Bistable reaction-diffusion on a network},
author = {J. -G. Caputo and G. Cruz-Pacheco and P. Panayotaros},
journal= {arXiv preprint arXiv:1406.7742},
year = {2015}
}