Strong Effects of Network Architecture in the Entrainment of Coupled Oscillator Systems

TL;DR

This paper investigates how network architecture influences the ability of coupled oscillator systems to synchronize with external signals, revealing that hierarchical and directional biases significantly affect entrainment efficiency.

Contribution

It provides analytical and numerical evidence that network structure, especially hierarchy and directionality, critically impacts oscillator entrainment, and introduces evolutionary methods to optimize such networks.

Findings

Entrainment window narrows exponentially with increased hierarchy.

Directional bias in networks enhances entrainment.

Evolutionary optimization can create networks with high entrainment ability.

Abstract

Entrainment of randomly coupled oscillator networks by periodic external forcing applied to a subset of elements is numerically and analytically investigated. For a large class of interaction functions, we find that the entrainment window with a tongue shape becomes exponentially narrow for networks with higher hierarchical organization. However, the entrainment is significantly facilitated if the networks are directionally biased, i.e., closer to the feedforward networks. Furthermore, we show that the networks with high entrainment ability can be constructed by evolutionary optimization processes. The neural network structure of the master clock of the circadian rhythm in mammals is discussed from the viewpoint of our results.