Complex phase space of a simple synchronization model

TL;DR

This paper thoroughly investigates the phase space of a simple two-mode stochastic oscillator synchronization model, revealing complex behaviors and partial synchronization under various conditions.

Contribution

It uncovers the complex phase space structure and identifies conditions for partial synchronization in a simple pulse-coupled oscillator model.

Findings

Multiple phases with distinct periodic signals identified

Partial synchronization occurs under broad conditions

Complex phase space depends on optimization threshold and oscillation periods

Abstract

The phase-space of a simple synchronization model is thoroughly investigated. The model considers two-mode stochastic oscillators, coupled through a pulse-like interaction controlled by simple optimization rules. A complex phase space is uncovered as a function of two relevant model parameters that are related to the optimization threshold and the periods of the two oscillation modes. Several phases with different periodic global output signals are identified. It is shown that the system exhibits partial synchronization under unexpectedly general conditions.