A new necessary condition for Turing instabilities

被引：4

作者：

Elragig, Aiman ^{[2
]}

Townley, Stuart ^{[1
]}

机构：

[1] Univ Exeter, Coll Engn Math & Phys Sci, Environm & Sustainabil Inst, Exeter EX4 4QJ, Devon, England

[2] Univ Exeter, Coll Engn Math & Phys Sci, Math Res Inst, Exeter EX4 4QJ, Devon, England

来源：

MATHEMATICAL BIOSCIENCES | 2012年 / 239卷 / 01期

关键词：

Lyapunov function; Diffusion driven (Turing) instability; Reactivity; Semi-definite programming; PATTERN-FORMATION; REACTION-DIFFUSION; SPATIAL-PATTERN; SYSTEMS; MODELS; HETEROGENEITY; OSCILLATIONS; STABILITY; DYNAMICS;

D O I：

10.1016/j.mbs.2012.04.006

中图分类号：

Q [生物科学];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

Reactivity (a.k.a initial growth) is necessary for diffusion driven instability (Turing instability). Using a notion of common Lyapunov function we show that this necessary condition is a special case of a more powerful (i.e. tighter) necessary condition. Specifically, we show that if the linearised reaction matrix and the diffusion matrix share a common Lyapunov function, then Turing instability is not possible. The existence of common Lyapunov functions is readily checked using semi-definite programming. We apply this result to the Gierer-Meinhardt system modelling regenerative properties of Hydra, the Oregonator, to a host-parasite-hyperparasite system with diffusion and to a reaction-diffusion-chemotaxis model for a multi-species host-parasitoid community. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：131 / 138

页数：8