Generalized Voter-like model on activity driven networks with attractiveness

TL;DR

This paper analyzes a generalized consensus model on activity-driven networks with attractiveness, deriving equations for consensus time and exit probability, and highlights the impact of temporal network dynamics on voter-like processes.

Contribution

It introduces a heterogeneous mean-field approach to a generalized voter/Moran model on activity-driven networks with attractiveness, providing analytical insights and comparisons with simulations.

Findings

Excellent agreement between analytical results and simulations.

Symmetry observed between voter and Moran dynamics in different network types.

Temporal network dynamics significantly influence consensus processes.

Abstract

We study the behavior of a generalized consensus dynamics on a temporal network of interactions, the activity driven network with attractiveness. In this temporal network model, agents are endowed with an intrinsic activity $a$, ruling the rate at which they generate connections, and an intrinsic attractiveness $b$, modulating the rate at which they receive connections. The consensus dynamics considered is a mixed voter/Moran dynamics. Each agent, either in state $0$ or $1$, modifies his/her state when connecting with a peer. Thus, an active agent copies his/her state from the peer (with probability $p$) or imposes his/her state to him/her (with the complementary probability $1-p$). Applying a heterogeneous mean-field approach, we derive a differential equation for the average density of voters with activity $a$ and attractiveness $b$ in state $1$, that we use to evaluate the average time to reach consensus and the exit probability, defined as the probability that a single agent with activity $a$ and attractiveness $b$ eventually imposes his/her state to a pool of initially unanimous population in the opposite state. We study a number of particular cases, finding an excellent agreement with numerical simulations of the model. Interestingly, we observe a symmetry between voter and Moran dynamics in pure activity driven networks and their static integrated counterparts that exemplifies the strong differences that a time-varying network can impose on dynamical processes.