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Bulletin of Mathematical Biology

, Volume 55, Issue 2, pp 365–384 | Cite as

Diffusion driven instability in an inhomogeneous domain

  • Debbie L. Benson
  • Jonathan A. Sherratt
  • Philip K. Maini
Article

Abstract

Diffusion driven instability in reaction-diffusion systems has been proposed as a mechanism for pattern formation in numerous embryological and ecological contexts. However, the possible effects of environmental inhomogeneities has received relatively little attention. We consider a general two species reaction-diffusion model in one space dimension, with one diffusion coefficient a step function of the spatial coordinate. We derive the dispersion relation and the solution of the linearized system. We apply our results to Turing-type models for both embryogenesis and predator-prey interactions. In the former case we derive conditions for pattern to be isolated in one part of the domain, and in the latter we introduce the concept of “environmental instability”. Our results suggest that environmental inhomogeneity could be an important regulator of biological pattern formation.

Keywords

Dispersion Relation Marginal Stability Linear Solution Flux Boundary Condition Homogeneous Steady State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Society for Mathematical Biology 1992

Authors and Affiliations

  • Debbie L. Benson
    • 1
  • Jonathan A. Sherratt
    • 1
  • Philip K. Maini
    • 1
  1. 1.Centre for Mathematical BiologyMathematical InstituteOxfordUK

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