Control strategies and trends to equilibrium for kinetic models of opinion dynamics driven by social activity

TL;DR

This paper develops kinetic models of opinion dynamics based on social activity levels, showing how social interactions influence opinion polarization and consensus, and proposes control strategies to promote social activity and convergence to equilibrium.

Contribution

It introduces new kinetic equations incorporating social activity, analyzes opinion polarization and consensus phenomena, and proposes control strategies with convergence proofs using entropy methods.

Findings

Opinion polarization occurs among low-activity individuals.

Active individuals tend to develop consensus.

Control strategies can effectively increase social activity and promote equilibrium.

Abstract

We introduce new kinetic equations modeling opinion dynamics inside a population of individuals, whose propensity to interact with each other is described by their level of social activity. We show that opinion polarization can arise among agents with a low activity level, while active ones develop a consensus, highlighting the importance of social interactions to prevent the formation of extreme opinions. Moreover, we present a realistic control strategy aimed at reducing the number of inactive agents and increasing the number of socially active ones. At last, we prove several (weak and strong) convergence to equilibrium results for such controlled model. In particular, by considering additional interactions between individuals and opinion leaders capable of steering the average opinion of the population, we use entropy method-like techniques to estimate the relaxation toward equilibrium of solutions to a Fokker--Planck equation with degenerate time-dependent coefficients.