Opinion Dynamics on Activity-driven Networks

The activity-driven network model offers a minimal yet realistic description of systems where connectivity arises from heterogeneous individual activation rather than static links. Applying an opinion model to these networks reveals how activity patterns and social noise interact to produce collective order and disorder in social systems. In this study, we investigate the majority-vote model on activity-driven networks. In this opinion framework, each agent adopts one of two possible states, represented by the stochastic variable σ = +1 or -1, and tends to align it with the local majority. The social noise parameter q quantifies the probability of adopting an opinion opposite to the prevailing local one. Agents are represented by nodes in the activity-driven network while links stand for the social interactions among them. We construct activity-driven networks by activating each node according to their individual rates and connecting each active node to m randomly selected others, avoiding self-loops and multiple links. The resulting integrated network reflects the cumulative structural patterns emerging from the activity-driven wiring dynamics. We perform Monte Carlo simulations to compute key physical observables such as the average magnetization, susceptibility, and Binder cumulant. The results reveal a continuous order disorder phase transition whose critical value of q that depends on the connectivity structure integrated by activated nodes. These findings highlight the crucial role of activity-driven connectivity patterns in shaping consensus formation, providing a modeling perspective for understanding opinion dynamics and critical behavior in irreversible systems in networks.