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....
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2005
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| In: |
Journal of mathematical biology
Year: 2004, Volume: 50, Issue: 1, Pages: 49-66 |
| ISSN: | 1432-1416 |
| DOI: | 10.1007/s00285-004-0279-1 |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1007/s00285-004-0279-1 Verlag, Volltext: https://link.springer.com/article/10.1007/s00285-004-0279-1 
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| Author Notes: | Daniela Morale, Vincenzo Capasso, Karl Oelschläger |
| Summary: | 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). |
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| Item Description: | First online: 05 July 2004 Gesehen am 13.06.2018 |
| Physical Description: | Online Resource |
| ISSN: | 1432-1416 |
| DOI: | 10.1007/s00285-004-0279-1 |