An interacting particle system modelling aggregation behavior: from individuals to populations.
In this paper we investigate the stochastic modelling of a spatially structured biological population subject to social interaction. The biological motivation comes from the analysis of field experiments on a species of ants which exhibits a clear tendency to aggregate, still avoiding overcrowding. The model we propose here provides an explanation of this experimental behavior in terms of "long-ranged" aggregation and "short-ranged" repulsion mechanisms among individuals, in addition to an individual random dispersal described by a Brownian motion. Further, based on a "law of large numbers", we discuss the convergence, for large N, of a system of stochastic differential equations describing the evolution of N individuals (Lagrangian approach) to a deterministic integro-differential equation describing the evolution of the mean-field spatial density of the population (Eulerian approach).
Morale
Daniela
D
MIRIAM & Department of Mathematics, University of Milan, Italy. morale@mat.unimi.it
Capasso
Vincenzo
V
Oelschläger
Karl
K
D000818:Animals; D001000:Ants; D008954:Models, Biological; D011157:Population Dynamics; D012919:Social Behavior; D013269:Stochastic Processes