Hierarchical structure induced by external input in coevolving dynamical networks

Abstract

We investigate a coevolving network of coupled maps subject to a forcing as a simple model for an adaptive system of neurons receiving an external stimulus. Coevolution means that the dynamics of the maps modifies the connectivity structure of the underlying network, and that this structure in turn affects the dynamics, both varying in time. The local dynamics is chaotic and described by the circle map. The influence of the intensity of the external stimulus on the dynamical collective behavior and the topological properties of the network are studied. It is shown that there are ranges of the intensity of the stimulus for which hierarchical structures arise in the network. In addition, it is found that the stimulus induces more structure when the states of the maps are less synchronized. Our work illustrates the potential of coupled map models for studying coevolution in complex systems