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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 when movement behavior is uncertain. The model consists of a system of partial differential equations whose parameters reflect the movement behavior of individuals within each pack and whose steady-state 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, we show that solving a nonzero-sum differential game corresponds to finding a non-invasible function-valued trait. From the ecological standpoint, when movement behavior is uncertain, the resulting evolutionarily stable equilibrium gives rise to a buffer-zone, or a no-wolf's land where deer are known to find refuge.
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Submitted on : Friday, May 29, 2020 - 10:38:46 PM
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Frédéric Hamelin, Mark Lewis. A differential game theoretical analysis of mechanistic models for territoriality. Journal of Mathematical Biology, Springer Verlag (Germany), 2009, 61 (5), pp.665-694. ⟨10.1007/s00285-009-0316-1⟩. ⟨hal-02655608⟩



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