Noisy voter models in switching environments

• Main Authors: Caligiuri, Annalisa, Galla, Tobias
• Format: Journal Article
• Language: English
• Published: 30.05.2023
• Subjects: Physics - Physics and Society; Physics - Statistical Mechanics
• DOI: 10.48550/arxiv.2305.19096

We study the stationary states of variants of the noisy voter model, subject to fluctuating parameters or external environments. Specifically, we consider scenarios in which the herding-to-noise ratio switches randomly and on different time scales between two values. We show that this can lead to a phase in which polarised and heterogeneous states exist. Secondly, we analyse a population of noisy voters subject to groups of external influencers, and show how multi-peak stationary distributions emerge. Our work is based on a combination of individual-based simulations, analytical approximations in terms of a piecewise-deterministic Markov processes (PDMP), and on corrections to this process capturing intrinsic stochasticity in the linear-noise approximation. We also propose a numerical scheme to obtain the stationary distribution of PDMPs with three environmental states and linear velocity fields.