Analysis of a continuous-time adaptive voter model.

Abstract

In this paper, we study a variant of the voter model on adaptive networks in which nodes can flip their spin, create new connections, or break existing connections. We first perform an analysis based on the mean-field approximation to compute asymptotic values for macroscopic estimates of the system, namely, the total mass of present edges in the system and the average spin. However, numerical results show that this approximation is not very suitable for such a system, for which it does not capture key features such as the network breaking into two disjoint and opposing (in spin) communities. Therefore, we propose another approximation based on an alternate coordinate system to improve accuracy and validate this model through simulations. Finally, we state a conjecture dealing with the qualitative properties of the system, corroborated by numerous numerical simulations.