Self-Organization in Space and Induced by Fluctuations

We present a simple discrete model for the non-linear spatial interaction of different kinds of “subpopulations” composed of identical moving entities like particles, bacteria, individuals, etc. The model allows to mimic a variety of self-organized agglomeration and segregation phenomena. By relating it to game-theoretical ideas, it can be applied not only to attractive and repulsive interactions in physical and chemical systems, but also to the much richer combinations of positive and negative interactions found in biological and socio-economic systems. Apart from investigating symmetric interactions related to a continuous increase of the “overall success” within the system (“self-optimization”), we will focus on cases, where fluctuations further or induce self-organization, even though the initial conditions and the interactions are assumed homogeneous in space (translation invariant).