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. [10.1007/s00285-004-0279-1]

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

D. Morale
Primo
;
V. Capasso
Secondo
;
2005

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).
Agent based models ; Aggregation ; Self-organization ; Stochastic differential equations ; Moderate limit ; Empirical measures
Settore MAT/06 - Probabilita' e Statistica Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/5093
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