Aging in coevolving voter models

Abstract

Aging, understood as the tendency to remain in a given state the longer the persistence time in that state, plays a crucial role in the dynamics of complex systems. In this paper, we explore the influence of aging on coevolution models, that is, models in which the dynamics of the states of the nodes in a complex network is coupled to the dynamics of the structure of the network. In particular we consider the coevolving voter model, and we introduce two versions of this model that include aging effects: the Link Aging Model (LAM) and the Node Aging Model (NAM). In the LAM, aging is associated with the persistence time of a link in the evolving network, while in the NAM, aging is associated with the persistence time of a node in a given state. We show that aging significantly affects the absorbing phase transition of the coevolution voter model, shifting the transition point in opposite directions for the LAM and NAM. We also show that the generic absorbing phase transition can disappear due to aging effects.