General coevolution ot topology and dynamics in networks

Abstract

We present a general framework for the study of coevolution in dynamical systems. This phenomenon consists of the coexistence of two dynamical processes on networks of interacting elements: node state change and rewiring of links between nodes. The process of rewiring is described in terms of two basic actions: disconnection and reconnection between nodes, both based on a mechanism of comparison of their states. Different rewiring rules can be expressed in this scheme. We assume that each process, rewiring and node state change, occurs with its own probability, independently from the other. The collective behavior of a coevolutionary system is characterized in the space of parameters given by these two probabilities. As an application, for a voterlike node dynamics we find that reconnections between nodes with similar states lead to network fragmentation. The critical boundaries for the onset of fragmentation in networks with different properties are calculated on this space. We show that coevolution models correspond to curves on this space, describing coupling relations between the probabilities for the two processes. The occurrence of network fragmentation transitions are predicted for diverse models, and agreement is found with some earlier results