Continuous and discontinuous phase transitions and partial synchronization in stochastic three-state oscillators

TL;DR

This paper explores how stochastic three-state oscillators undergo both continuous and discontinuous synchronization transitions, influenced by coupling and disorder, revealing complex behaviors including partial synchronization and frequency measurement subtleties.

Contribution

It demonstrates how simple stochastic oscillator models can exhibit diverse synchronization phenomena, bridging understanding between simple and complex systems.

Findings

Transition type depends on coupling and disorder.

Partial synchronization occurs above the threshold.

Frequency measurements can be counterintuitive.

Abstract

We investigate both continuous (second-order) and discontinuous (first-order) transitions to macroscopic synchronization within a single class of discrete, stochastic (globally) phase-coupled oscillators. We provide analytical and numerical evidence that the continuity of the transition depends on the coupling coefficients and, in some nonuniform populations, on the degree of quenched disorder. Hence, in a relatively simple setting this class of models exhibits the qualitative behaviors characteristic of a variety of considerably more complicated models. In addition, we study the microscopic basis of synchronization above threshold and detail the counterintuitive subtleties relating measurements of time averaged frequencies and mean field oscillations. Most notably, we observe a state of suprathreshold partial synchronization in which time-averaged frequency measurements from individual oscillators do not correspond to the frequency of macroscopic oscillations observed in the population.