|InterJournal Complex Systems, 2243
|Manuscript Number: |
Submission Date: 20080226
|Analysis of phase transition in a coevolution network model|
We have investigated a simple model on which network topology and state of nodes coevolve. Recently, Holme and Newman have proposed an adaptive voter model (Phys. Rev. E 74, 056108). In this model, each node has one of G opinions (G is a constant number). At each time step, randomly chosen node reattaches its link to randomly chosen node having same opinion with probability P, otherwise, adopts the opinion of one of its neighbors with probability 1-P. This model exhibits nonequilibrium phase transition from a regime in which almost all nodes have same opinion to one in which network splits into some groups having different opinion by changing parameter P. To explain this phenomenon, we consider here the simplest case in this model, namely, there are only two opinions. We have adopted a pairwise approximation to this model. In this approximation, we describe the process of opinion propagation or rewiring links as the time evolution of the number of the various types of connected pairs where the number of triples of nodes is approximated by the number of pairs and nodes, and, higher order structures are ignored. The analytical results from the pairwise approximation indicate the existence of a bifurcation. We find that this bifurcation strongly depends on the number of links in networks, not only P. The more links, the easier network is occupied by one opinion. We can derive the phase diagram about P and the number of links theoretically.
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