The Mathematical Institute, University of Oxford, Eprints Archive

Complex pattern formation in reaction diffusion systems with spatially-varying parameters

Page, K. M. and Maini, P. K. and Monk, N. A. M. (2005) Complex pattern formation in reaction diffusion systems with spatially-varying parameters. Physica D, 202 (1-2). pp. 95-115.

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Abstract

Spontaneous pattern formation in reaction–diffusion systems on a spatially homogeneous domain has been well studied. However, in embryonic development and elsewhere, pattern formation often takes place on a spatially heterogeneous background. We explore the effects of spatially varying parameters on pattern formation in one and two dimensions using the Gierer–Meinhardt reaction–diffusion model. We investigate the effect of the wavelength of a pre-pattern and demonstrate a novel form of moving pattern. We find that spatially heterogeneous parameters can both increase the range and complexity of possible patterns and enhance the robustness of pattern selection.

Item Type:Article
Uncontrolled Keywords:Spatially varying parameters; Gierer–Meinhardt reaction–diffusion; Turing space; Pattern formation; Self-organised spatial pattern
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:348
Deposited By:Philip Maini
Deposited On:10 Nov 2006
Last Modified:20 Jul 2009 14:20

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