Spatial patterns in population conflicts
| Autor: | V. Hutson, G.T. Vickers, C. J. Budd |
|---|---|
| Rok vydání: | 1993 |
| Předmět: |
education.field_of_study
Ecology Applied Mathematics Population Agricultural and Biological Sciences (miscellaneous) Instability Evolutionarily stable strategy Modeling and Simulation Reaction–diffusion system Spatial ecology Statistical physics Diffusion (business) Constant (mathematics) education Bifurcation Mathematics |
| Zdroj: | Journal of Mathematical Biology. 31:411-430 |
| ISSN: | 1432-1416 0303-6812 |
| DOI: | 10.1007/bf00163924 |
| Popis: | We consider a dynamical model for evolutionary games, and enquire how the introduction of diffusion may lead to the formation of stationary spatially inhomogeneous solutions, that is patterns. For the model equations being used it is already known that if there is an evolutionarily stable strategy (ESS), then it is stable. Equilibrium solutions which are not ESS's and which are stable with respect to spatially constant perturbations may be unstable for certain choices of the dispersal rates. We prove by a bifurcation technique that under appropriate conditions the instability leads to patterns. Computations using a curve-following technique show that the bifurcations exhibit a rich structure with loops joined by symmetry-breaking branches. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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