An interacting particle system modelling aggregation behavior: from individuals to populations

Authored by D Morale, V Capasso, K Oelschlager

Date Published: 2005-01

DOI: 10.1007/s00285-004-0279-1

Sponsors: No sponsors listed

Platforms: No platforms listed

Model Documentation: Other Narrative Mathematical description

Model Code URLs: Model code not found

Abstract

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).

Tags

Agent based models self-organization Aggregation Stochastic differential equations empirical measures moderate limit