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Article Dans Une Revue Physica D: Nonlinear Phenomena Année : 2015

Self-organized populations interacting under pursuit-evasion dynamics

Résumé

We discuss the modelling of interacting populations through pursuit-evasion ---- or attraction-repulsion ---- principles~: preys try to escape chasers, chasers are attracted by the presence of preys. We construct a hierarchy of models, ranging from ODEs systems with finite numbers of individuals of each population, to hydrodynamic systems. First order macroscopic models look like generalized ''two-species Keller-Segel equations''. But, due to cross--interactions, we can show that the system does not exhibit any blow up phenomena in finite time. We also obtain second order models, that have the form of systems of balance laws, derived from kinetic models. We bring out a few remarkable features of the models based either on mathematical analysis or numerical simulations.
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Dates et versions

hal-01070626 , version 1 (01-10-2014)

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  • HAL Id : hal-01070626 , version 1

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Thierry Goudon, Boniface Nkonga, Michel Rascle, Magali Ribot. Self-organized populations interacting under pursuit-evasion dynamics. Physica D: Nonlinear Phenomena, 2015, 304-305, pp.41. ⟨hal-01070626⟩
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