Self-Organization of Networks

Abstract

The previous chapter showed how the model of Brownian agents with an internal parameter θ_i can be used to simulate structures in reaction-diffusion systems. In this chapter, we want to explore this idea further: the internal parameter θ_i ∈ −1, 0, +1 shall describe three different responses to the components of an effective field that can be further changed by Brownian agents, depending on their actual value of θ_i(t). The internal energy depot as another internal degree of freedom shall not be considered here. The model shall be applied to the generation of a specific pattern, which can be denoted as a network of links among arbitrary nodes. The self-organized formation of links among a set of nodes is of interest in many different fields. In electronic engineering, for instance, one is interested in self-assembly and self-repair of electrical circuits, and in biology, models for self-wiring and neuronal networks are investigated. On the social level, the self-organization of trail networks among different destinations is a similar problem, which will be discussed in detail in Sects. 5.4 and 6.2. The establishment of connections on demand in telecommunication or logistics is also related to the problem discussed here.