General coevolution of 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. We assume that the process of rewiring and node state change occur with probabilities Pr and Pc respectively, independent of each other. The collective behavior of a coevolutionary system can be characterized on the space of parameters (Pr, Pc). 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 functional relations between Pr and Pc. The occurrence of a one-large-domain phase and a fragmented phase in the network is predicted for diverse models, and agreement is found with some earlier results. The collective behavior of system is also characterized on the space of parameters for the disconnection and reconnection actions. In a region of this space, we find a behavior where different node states can coexist for very long times on one large, connected network.

Graph fission in an evolving voter model

“…Our starting point is the model of Holme and Newman (38)(39)(40)(41). They begin with a network of N vertices and M edges, where each vertex x has an opinion ξðxÞ from a set of G possible opinions and the number of people per opinion γ N ¼ N∕G stays bounded as N gets large.…”

Detecting and describing dynamic equilibria in adaptive networks

“…More recently, allowing for the coevolution of network structure and node-state dynamics has given rise to abundant literature on adaptive networks [5,6], capturing such diverse phenomena as the emergence of cooperation [7,8,9,10,11,12], opinion formation [13,14,15,16], disease spreading [17,18,19,20,21], speciation [22,23] and traffic flows [24,25,26]. While some contributions explore the respective phenomenology with individualbased simulations [8,10,27,28], others also focus on providing explanatory frameworks for observed dynamics [7,9,11,15,19,20,29].…”

Emergence of communities in a coevolutive model of wealth exchange

“…a coevolutionary dynamic system where agents can change their neighborhood and these topological changes have effects on the dynamics of the agents. The model can fit into the general framework for systems with coevolution between topology and dynamics [15] as a DR process, i.e. a process with a rewiring dynamic where disconnect actions are governed by a dissimilarity mechanism (D) and reconnection actions are governed by a random mechanism (R).…”