Journal
PHYSICA D-NONLINEAR PHENOMENA
Volume 202, Issue 1-2, Pages 95-115Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.physd.2005.01.022
Keywords
spatially varying parameters; Gierer-Meinhardt reaction-diffusion; turing space; pattern formation; self-organised spatial pattern
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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. (c) 2005 Elsevier B.V. All rights reserved.
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