Topology, noise, and parallel updates in circular opinion dynamics

TL;DR

This paper investigates a circular opinion dynamics model with local interactions and parallel updates, revealing how noise influences topological states and induces switching behavior, with implications for understanding opinion formation.

Contribution

It introduces a model combining topology, noise, and parallel updates in opinion dynamics, and analyzes how noise destabilizes topological states and causes regime switching.

Findings

Noise destabilizes winding states.

Noise induces flip-flop switching between orientations.

Order parameters distinguish topological trapping from symmetry breaking.

Abstract

We study a circular opinion dynamics model with local midpoint interactions, extended to allow parallel updates of multiple sites. On a ring, the dynamics admits twisted states associated with integer winding numbers. We investigate how bi-modal noise, which drives opinions toward two antipodal directions, affects these configurations. Numerically, we find that noise both destabilizes winding states and induces a flip--flop regime, characterized by macroscopic switching between preferred orientations. We introduce order parameters that distinguish topological trapping from symmetry breaking, providing a simple macroscopic description of the dynamics.