Complex dynamics of a nonlinear voter model with contrarian agents

TL;DR

This paper explores the complex mean-field dynamics of a nonlinear opinion model with congregator and contrarian agents, revealing rich bifurcation phenomena including multiple equilibria and limit cycles.

Contribution

It introduces a nonlinear voter model incorporating contrarians and analyzes its bifurcation structure, highlighting novel dynamic behaviors.

Findings

Rich bifurcation scenarios identified

Existence of multiple stable equilibria and limit cycles

Contrarians significantly influence opinion dynamics

Abstract

We investigate mean-field dynamics of a nonlinear opinion formation model with congregator and contrarian agents. Each agent assumes one of the two possible states. Congregators imitate the state of other agents with a rate that increases with the number of other agents in the opposite state, as in the linear voter model and nonlinear majority voting models. Contrarians flip the state with a rate that increases with the number of other agents in the same state. The nonlinearity controls the strength of the majority voting and is used as a main bifurcation parameter. We show that the model undergoes a rich bifurcation scenario comprising the egalitarian equilibrium, two symmetric lopsided equilibria, limit cycle, and coexistence of different types of stable equilibria with intertwining attrative basins.