The Mathematical Institute, University of Oxford, Eprints Archive

Parameter domains for Turing and stationary flow-distributed waves: I. The influence of nonlinearity

Satnoianu, R. A. and Maini, P. K. and Menzinger, M. (2001) Parameter domains for Turing and stationary flow-distributed waves: I. The influence of nonlinearity. Physica D, 160 (1-2). pp. 79-102.

[img]
Preview
PDF
320Kb

Abstract

new type of instability in coupled reaction-diffusion-advection systems is analysed in a one-dimensional domain. This instability, arising due to the combined action of flow and diffusion, creates spatially periodic stationary waves termed flow and diffusion-distributed structures (FDS). Here we show, via linear stability analysis, that FDS are predicted in a considerably wider domain and are more robust (in the parameter domain) than the classical Turing instability patterns. FDS also represent a natural extension of the recently discovered flow-distributed oscillations (FDO). Nonlinear bifurcation analysis and numerical simulations in one-dimensional spatial domains show that FDS also have much richer solution behaviour than Turing structures. In the framework presented here Turing structures can be viewed as a particular instance of FDS. We conclude that FDS should be more easily obtainable in chemical systems than Turing (and FDO) structures and that they may play a potentially important role in biological pattern formation.

Item Type:Article
Uncontrolled Keywords:Flow-distributed structures (FDS); Flow-distributed oscillations (FDO); Differential-flow instability (DIFI); Turing instability; Stationary space-periodic patterns; Hopf instability; Quadratic and cubic autocatalysis
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:403
Deposited By:Philip Maini
Deposited On:20 Nov 2006
Last Modified:20 Jul 2009 14:21

Repository Staff Only: item control page