Published June 1981
| public
Journal Article
A generalized diffusion model for growth and dispersal in a population
- Creators
- Cohen, Donald S.
- Murray, James D.
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.
Additional Information
© 1981 Springer-Verlag. Received 17 September 1980; Revised 20 January 1981; Issue Date June 1981. 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.Additional details
- Eprint ID
- 100684
- DOI
- 10.1007/bf00276132
- Resolver ID
- CaltechAUTHORS:20200113-132911745
- GR/B31378
- Science Research Council (SRC)
- Created
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2020-01-13Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field