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.
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.
|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|
|Deposited By:||Philip Maini|
|Deposited On:||10 Nov 2006|
|Last Modified:||20 Jul 2009 14:20|
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