# Temporal self-similar synchronization patterns and scaling in repulsively coupled oscillators

## TL;DR

This paper investigates synchronization patterns in repulsively coupled oscillators, revealing self-similar temporal patterns and scaling behaviors influenced by disorder in natural frequencies, with implications for understanding complex dynamical systems.

## Contribution

It introduces the discovery of self-similar, temporally scaling synchronization patterns in repulsively coupled oscillators under frequency disorder, highlighting new dynamical phenomena.

## Key findings

- Limit cycles with long periods emerge due to frequency disorder.
- Sequences of self-similar phase-locked patterns are observed.
- Periods scale with the inverse width of the frequency distribution.

## Abstract

We study synchronization patterns in repulsively coupled Kuramoto oscillators and focus on the impact of disorder in the natural frequencies. Among other choices we select the grid size and topology in a way that we observe a dynamically induced dimensional reduction with a continuum of attractors as long as the natural frequencies are uniformly chosen. When we introduce disorder in these frequencies, we find limit cycles with periods that are orders of magnitude longer than the natural frequencies of individual oscillators. Moreover we identify sequences of temporary patterns of phase-locked motion, which are self-similar in time and whose periods scale with a power of the inverse width about a uniform frequency distribution. This behavior provides challenges for future research.