Logarithmic Lipschitz norms and diffusion-induced instability
Systems and Control
2012-08-03 v2 Analysis of PDEs
Abstract
This paper proves that contractive ordinary differential equation systems remain contractive when diffusion is added. Thus, diffusive instabilities, in the sense of the Turing phenomenon, cannot arise for such systems. An important biochemical system is shown to satisfy the required conditions.
Cite
@article{arxiv.1208.0326,
title = {Logarithmic Lipschitz norms and diffusion-induced instability},
author = {Zahra Aminzare and Eduardo D. Sontag},
journal= {arXiv preprint arXiv:1208.0326},
year = {2012}
}