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A generalized diffusion model for growth and dispersal in a population

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Abstract

A reaction-diffusion model is presented in which spatial structure is maintained by means of a diffusive mechanism more general than classical Fickian diffusion. This generalized diffusion takes into account the diffusive gradient (or gradient energy) necessary to maintain a pattern even in a single diffusing species. The approach is based on a Landau-Ginzburg free energy model. A problem involving simple logistic kinetics is fully analyzed, and a nonlinear stability analysis based on a multi-scale perturbation method shows bifurcation to non-uniform states.

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Authors and Affiliations

  1. Department of Applied Mathematics, California Institute of Technology, 91125, Pasadena, CA, USA

    Donald S. Cohen

  2. Mathematical Institute, Oxford University, Oxford, England

    James D. Murray

Authors
  1. Donald S. Cohen
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  2. James D. Murray
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Part of this work was done while at the Mathematical Institute, Oxford University as a Senior Visiting Fellow supported by the Science Research Council of Great Britain under grant GR/B31378

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Cohen, D.S., Murray, J.D. A generalized diffusion model for growth and dispersal in a population. J. Math. Biology 12, 237–249 (1981). https://doi.org/10.1007/BF00276132

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  • DOI: https://doi.org/10.1007/BF00276132

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