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).
An interacting particle system modelling aggregation behavior : from individuals to populations / D. Morale, V. Capasso, K. Oelschläger. - In: JOURNAL OF MATHEMATICAL BIOLOGY. - ISSN 0303-6812. - 50:1(2005), pp. 49-66.
|Titolo:||An interacting particle system modelling aggregation behavior : from individuals to populations|
MORALE, DANIELA (Primo)
CAPASSO, VINCENZO (Secondo)
|Parole Chiave:||Agent based models ; Aggregation ; Self-organization ; Stochastic differential equations ; Moderate limit ; Empirical measures|
|Settore Scientifico Disciplinare:||Settore MAT/06 - Probabilita' e Statistica Matematica|
|Data di pubblicazione:||2005|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1007/s00285-004-0279-1|
|Appare nelle tipologie:||01 - Articolo su periodico|