Entrainment of randomly coupled oscillator networks by a pacemaker

TL;DR

This paper investigates how a pacemaker influences random oscillator networks, revealing that the ability to entrain depends exponentially on network depth, with analytical support for large asymmetric networks.

Contribution

It introduces a quantitative analysis of entrainment in random oscillator networks, highlighting the exponential relationship between network depth and entrainment window, supported by analytical derivation.

Findings

Entrainment window decreases exponentially with network depth.

Shallow networks are more likely to lock to the pacemaker.

Analytical approximation confirms exponential dependence in large networks.

Abstract

Entrainment by a pacemaker, representing an element with a higher frequency, is numerically investigated for several classes of random networks which consist of identical phase oscillators. We find that the entrainment frequency window of a network decreases exponentially with its depth, defined as the mean forward distance of the elements from the pacemaker. Effectively, only shallow networks can thus exhibit frequency-locking to the pacemaker. The exponential dependence is also derived analytically as an approximation for large random asymmetric networks.