Double transition in kinetic exchange opinion models with activation dynamics

TL;DR

This paper introduces a kinetic exchange opinion model with activation dynamics, revealing two distinct nonequilibrium phase transitions and three phases, including an absorbing state where all agents become inactive.

Contribution

It presents a novel opinion dynamics model incorporating activation/deactivation, and analytically and numerically identifies two phase transitions and the conditions for an absorbing inactive state.

Findings

Identification of two nonequilibrium phase transitions.

Existence of three phases: ordered, disordered, and absorbing.

Critical activation probability $w_c$ for the absorbing phase.

Abstract

In this work we study a model of opinion dynamics considering activation/deactivation of agents. In other words, individuals are not static and can become inactive and drop out from the discussion. A probability $w$ governs the deactivation dynamics, whereas social interactions are ruled by kinetic exchanges, considering competitive positive/negative interactions. Inactive agents can become active due to interactions with active agents. Our analytical and numerical results show the existence of two distinct nonequilibrium phase transitions, with the occurrence of three phases, namely ordered (ferromagnetic-like), disordered (paramagnetic-like) and absorbing phases. The absorbing phase represents a collective state where all agents are inactive, i.e., they do not participate on the dynamics, inducing a frozen state. We determine the critical value $w_c$ above which the system is in the absorbing phase independently of the other parameters. We also verify a distinct critical behavior for the transitions among different phases.