The role of intermediaries in the synchronization of pulse-coupled oscillators

TL;DR

This paper investigates how intermediaries affect synchronization in groups of pulse-coupled oscillators, revealing a novel discontinuous relationship between synchronization time and coupling strength.

Contribution

It introduces a new understanding of the collective behavior of LCOs with a third intermediary, showing a discontinuous synchronization phenomenon not seen in pairwise coupling.

Findings

Discontinuous relationship between synchronization time and coupling strength.

Robustness of the phenomenon across different initial conditions.

Mechanism for the discontinuities explained.

Abstract

The role of intermediaries in the synchronization of small groups of light controlled oscillators (LCO) is addressed. A single LCO is a two-time-scale phase oscillator. When pulse-coupling two LCOs, the synchronization time decreases monotonously as the coupling strength increases, independent of the initial conditions and frequency detuning. In this work we study numerically the effects that a third LCO induces to the collective behavior of the system. We analyze the new system by dealing with directed heterogeneous couplings among the units. We report a novel and robust phenomenon, absent when coupling two LCOs, which consists of a discontinuous relationship between the synchronization time and coupling strength or initial conditions. The mechanism responsible for the appearance of such discontinuities is discussed.