Influence of topology in the mobility enhancement of pulse-coupled oscillator synchronization

TL;DR

This paper investigates how the network topology influences the nonmonotonic synchronization time behavior in mobile pulse-coupled oscillators, identifying conditions that lead to predictable nonmonotonicity based on connectivity features.

Contribution

It introduces a control parameter to predict nonmonotonic behavior and links it to specific connectivity patterns and frustrated clusters in mobile PCO systems.

Findings

NMB occurs under sparse, non reciprocal interaction patterns.

Presence of frustrated clusters correlates with NMB.

A control parameter predicts the velocity range of NMB.

Abstract

In this work we revisit the nonmonotonic behavior (NMB) of synchronization time with velocity reported for systems of mobile pulse-coupled oscillators (PCOs). We devise a control parameter that allows us to predict in which range of velocities NMB may occur, also uncovering the conditions allowing us to establish the emergence of NMB based on specific features of the connectivity rule. Specifically, our results show that if the connectivity rule is such that the interaction patterns are sparse and, more importantly, include a large fraction of non reciprocal interactions, then the system will display NMB. We furthermore provide a microscopic explanation relating the presence of such features of the connectivity patterns to the existence of local clusters unable to synchronize, termed frustrated clusters, for which we also give a precise definition in terms of simple graph concepts. We conclude that, if the probability of finding a frustrated cluster in a system of moving PCOs is high enough, NMB occurs in a predictable range of velocities.