Doppler synchronization of pulsating phases by time delay

TL;DR

This paper analytically studies how oscillators exchanging finite pulses synchronize in networks, showing that any non-zero time lag leads to complete synchronization, with faster synchronization as the lag increases.

Contribution

It provides an analytical framework for pulse-based synchronization considering finite pulse widths and time delays, extending beyond previous integrate-and-fire models.

Findings

Complete synchronization occurs for any number of oscillators with suitable network conditions.

Synchronization time decreases as the time lag between oscillators increases.

The study offers insights into pulse exchange synchronization in biological and engineered systems.

Abstract

Synchronization by exchange of pulses is a widespread phenomenon, observed in flashing fireflies, applauding audiences and the neuronal network of the brain. Hitherto the focus has been on integrate-and-fire oscillators. Here we consider entirely analytic time evolution. Oscillators exchange narrow but finite pulses. For any non-zero time lag between the oscillators complete synchronization occurs for any number of oscillators arranged in interaction networks whose adjacency matrix fulfils some simple conditions. The time to synchronization decreases with increasing time lag.