An interacting particle system modelling aggregation behavior

• Verfasst von: Morale, Daniela [VerfasserIn]
• Verfasst von: Capasso, Vincenzo [VerfasserIn]
• Verfasst von: Oelschläger, Karl [VerfasserIn]
• Titel: An interacting particle system modelling aggregation behavior
• Titelzusatz: from individuals to populations
• Verf.angabe: Daniela Morale, Vincenzo Capasso, Karl Oelschläger
• Jahr des Originals: 2004
• Umfang: 18 S.
• Fussnoten: First online: 05 July 2004 ; Gesehen am 13.06.2018
• Titel Quelle: Enthalten in: Journal of mathematical biology
• Jahr Quelle: 2005
• Band/Heft Quelle: 50(2005), 1, S. 49-66
• ISSN Quelle: 1432-1416
• DOI: doi:10.1007/s00285-004-0279-1
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1576322424

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).