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

In: Math Everywhere

Author

Listed:
  • 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)

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.

Suggested Citation

  • Vincenzo Capasso & Daniela Morale & Matteo Ortisi, 2007. "Long Time Behavior of a System of Stochastic Differential Equations Modelling Aggregation," Springer Books, in: Giacomo Aletti & Alessandra Micheletti & Daniela Morale & Martin Burger (ed.), Math Everywhere, pages 25-38, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-44446-6_3
    DOI: 10.1007/978-3-540-44446-6_3
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