Long Time Behavior of a System of Stochastic Differential Equations Modelling Aggregation

Vincenzo Capasso (), Daniela Morale () and Matteo Ortisi ()
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Vincenzo Capasso: University of Milano, ADAMSS (Advanced Applied Mathematical and Statistical Sciences) & Department of Mathematics
Daniela Morale: University of Milano, ADAMSS (Advanced Applied Mathematical and Statistical Sciences) & Department of Mathematics
Matteo Ortisi: University of Milano, ADAMSS (Advanced Applied Mathematical and Statistical Sciences) & Department of Mathematics

A chapter in Math Everywhere, 2007, pp 25-38 from Springer

Abstract: Abstract In many biological settings it is possible to observe phenomena of pattern formation and clustering by cooperative individuals of a population. In biology and medicine there is a wide spectrum of examples which exhibit collective behavior, leading to self organization, with pattern formation. Aggregation patterns are usually explained in terms of forces, external and/or internal, acting upon individuals. Over the past couple of decades, a large amount of literature has been devoted to the mathematical modelling of self-organizing populations, based on the concepts of short-range/long-range “social interaction” at the individual level. The main interest has been in catching the main features of the interaction at the lower scale of single individuals that are responsible, at a larger scale, for a more complex behavior that leads to the formation of aggregating patterns.

Keywords: Invariant Measure; Particle System; Invariant Distribution; Interact Particle System; Past Couple (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/978-3-540-44446-6_3

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