Zealots in multistate noisy voter models

The noisy voter model is a stylized representation of opinion dynamics. Individuals copy opinions from other individuals, and are subject to spontaneous state changes. In the case two states this known have noise-driven transition between unimodal phase, in which both present, bimodal one dominates. presence zealots can remove phases with states. Here we study effects models $M>2$ on complete interaction graphs. We find that phase behavior diversifies, up six possible qualitatively different types stationary removes some these phases, but not all. analyze situations affect entire population, or only fraction agents, show situation corresponds single-community fractional number zealots, further enriching diagram. Our conducted analytically based effective birth-death dynamics for individuals holding given opinion. Results confirmed numerical simulations.