# Global synchronization of pulse-coupled oscillators on trees

arXiv: https://arxiv.org/abs/1604.08381 · HTML: https://mlsanity.com/paper/1604.08381/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Apr 2016.

## Built on by (most cited first, 1 of 1)

- [A latent linear model for nonlinear coupled oscillators on graphs](https://mlsanity.com/paper/2311.14910/) (2023)

## Abstract (arXiv)

Consider a distributed network on a finite simple graph G=(V,E) with diameter d and maximum degree Delta, where each node has a phase oscillator revolving on S1=ℝ/mathbbZ with unit speed. Pulse-coupling is a class of distributed time evolution rule for such networked phase oscillators inspired by biological oscillators, which depends only upon event-triggered local pulse communications. In this paper, we propose a novel inhibitory pulse-coupling and prove that arbitrary phase configuration on G synchronizes by time 51d if G is a tree and Delta ≤ 3. We extend this pulse-coupling by letting each oscillator throttle the input according to an auxiliary state variable. We show that the resulting adaptive pulse-coupling synchronizes arbitrary initial configuration on G by time 83d if G is a tree. As an application, we obtain a universal randomized distributed clock synchronization algorithm, which uses O(log Delta) memory per node and converges on any G with expected worst case running time of O(|V|+(d5+Delta2)log |V|).