Self-organized populations interacting under pursuit-evasion dynamics

Thierry Goudon 1 Boniface Nkonga 2 Michel Rascle 3 Magali Ribot 3, 4
2 CASTOR - Control, Analysis and Simulations for TOkamak Research
CRISAM - Inria Sophia Antipolis - Méditerranée
4 COFFEE - COmplex Flows For Energy and Environment
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR7351
Abstract : 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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Thierry Goudon, Boniface Nkonga, Michel Rascle, Magali Ribot. Self-organized populations interacting under pursuit-evasion dynamics. Physica D: Nonlinear Phenomena, Elsevier, 2015, 304-305, pp.41. ⟨hal-01070626⟩

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