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

Keiji Konishi | Zendy; Naoyuki Hara | Zendy

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

Author(s) -

Keiji Konishi,

Naoyuki Hara

Publication year - 2018

Publication title -

physical review. e

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.896

H-Index - 304

eISSN - 2470-0053

pISSN - 2470-0045

DOI - 10.1103/physreve.97.052201

Subject(s) - steady state (chemistry) , instability , turing , physics , stability (learning theory) , diffusion , amplitude , reaction–diffusion system , boundary (topology) , mechanics , statistical physics , classical mechanics , mathematical analysis , mathematics , computer science , thermodynamics , quantum mechanics , chemistry , machine learning , programming language

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.

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