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Stabilization of a spatially uniform steady state in two systems exhibiting Turing patterns.

Research paper by Keiji K Konishi, Naoyuki N Hara

Indexed on: 17 Jun '18Published on: 17 Jun '18Published in: Physical review. E



Abstract

This paper deals with the stabilization of a spatially uniform steady state in two coupled one-dimensional reaction-diffusion systems with Turing instability. This stabilization corresponds to amplitude death that occurs in a coupled system with Turing instability. Stability analysis of the steady state shows that stabilization does not occur if the two reaction-diffusion systems are identical. We derive a sufficient condition for the steady state to be stable for any length of system and any boundary conditions. Our analytical results are supported with numerical examples.