Long time behavior of a system of stochastic differential equations modelling aggregation

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.