Robust convergence in pulse coupled oscillators with delays

TL;DR

This paper demonstrates that pulse coupled oscillators with specific phase response curves can reliably synchronize on complex networks with delays, offering robust methods for sensor networks and biological systems.

Contribution

It introduces a class of phase response curves ensuring robust synchronization in delayed pulse coupled oscillators on arbitrary graphs, with explicit convergence bounds.

Findings

Oscillators with certain phase response curves synchronize reliably.

Synchronization occurs on arbitrary aperiodic connected graphs with delays.

Explicit bounds on convergence times are provided.

Abstract

We show that for pulse coupled oscillators a class of phase response curves with both excitation and inhibition exhibit robust convergence to synchrony on arbitrary aperiodic connected graphs with delays. We describe the basins of convergence and give explicit bounds on the convergence times. These results provide new and more robust methods for synchronization of sensor nets and also have biological implications.