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 P_{r} and P_{c}, respectively, independent of each other. The collective behavior of a coevolutionary system can be characterized on the space of parameters (P_{r}, P_{c}). 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 P_{r} and P_{c}. The occurrence of a onelargedomain 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 the 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.
 Publication:

EPL (Europhysics Letters)
 Pub Date:
 September 2011
 DOI:
 10.1209/02955075/95/58006
 arXiv:
 arXiv:1102.3467
 Bibcode:
 2011EL.....9558006H
 Keywords:

 Nonlinear Sciences  Adaptation and SelfOrganizing Systems;
 Condensed Matter  Statistical Mechanics;
 Nonlinear Sciences  Cellular Automata and Lattice Gases;
 Physics  Physics and Society
 EPrint:
 6 pages, 6 figures