A differential game theoretical analysis of mechanistic models for territoriality

Abstract : In this paper, elements of differential game theory are used to analyze a spatially explicit home range model for interacting wolf packs. The model consists of a system of partial differential equations whose parameters reflect the movement behavior of individuals within each pack and whose solutions describe the patterns of space-use associated to each pack. By controlling the behavioral parameters in a spatially-dynamic fashion, packs adjust their patterns of movement so as to find a Nash-optimal balance between spreading their territory and avoiding conflict with hostile neighbors. On the mathematical side, the game let appear some of the few singularities ever observed in nonzero-sum games. From the ecological standpoint, one recognizes in the resulting evolutionarily stable equilibrium a buffer-zone, or a no-wolf's land where deers are known to find refuge. Territories overlap arises as a singular solution. Scent-marking is not yet incorporated into the model.
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https://hal-agrocampus-ouest.archives-ouvertes.fr/hal-00729425
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Submitted on : Friday, September 7, 2012 - 3:41:26 PM
Last modification on : Wednesday, May 16, 2018 - 11:23:28 AM

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  • HAL Id : hal-00729425, version 1

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Frédéric Hamelin, M.A. Lewis. A differential game theoretical analysis of mechanistic models for territoriality. Journal of Mathematical Biology, Springer Verlag (Germany), 2010, 61 (5), pp.665-694. ⟨hal-00729425⟩

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