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arXiv · 2603.21838

Topology, noise, and parallel updates in a model of circular opinion dynamics

Wioletta M. Ruszel·Cristian Spitoni
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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.

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Wioletta M. Ruszel, Cristian Spitoni. 2026-03-23. Topology, noise, and parallel updates in a model of circular opinion dynamics. https://arxiv.org/abs/2603.21838

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