# Solitary States and Partial Synchrony in Oscillatory Ensembles with Attractive and Repulsive Interactions

## TL;DR

This paper investigates how networks of coupled oscillators transition between various synchronized states, including solitary and partially synchronous states, as the balance shifts from attraction to repulsion among elements.

## Contribution

It provides both numerical and analytical insights into the transitions between synchronous, solitary, and quasiperiodic states in oscillatory ensembles with mixed interactions.

## Key findings

- Identification of solitary states in oscillator networks
- Analysis of transitions driven by increasing repulsion
- Characterization of partially synchronous quasiperiodic dynamics

## Abstract

We numerically and analytically analyze transitions between different synchronous states in a network of globally coupled phase oscillators with attractive and repulsive interactions. The elements within the attractive or repulsive group are identical, but natural frequencies of the groups differ. In addition to a synchronous two-cluster state, the system exhibits a solitary state, when a single oscillator leaves the cluster of repulsive elements, as well as partially synchronous quasiperiodic dynamics. We demonstrate how the transitions between these states occur when the repulsion starts to prevail over attraction.