# Solitary states for coupled oscillators

## TL;DR

This paper investigates solitary states in networks of coupled oscillators, showing their widespread occurrence across different coupling types and conditions, and analyzing their bifurcation origins and coexistence regions.

## Contribution

It provides a comprehensive analysis of solitary states in various network configurations, including their creation via homoclinic bifurcation and conditions for their coexistence.

## Key findings

- Solitary states occur in local, non-local, and global coupled oscillator networks.
- Different types of solitary states are characterized by the number and arrangement of isolated oscillators.
- Homoclinic bifurcation leads to the creation of solitary states.

## Abstract

We demonstrate that solitary states can be widely observed for networks of coupled oscillators with local, non-local and global couplings, and they preserve in both thermodynamic and Hamiltonian limits. We show that depending on units' and network's parameters, different types of solitary states occur, characterized by the number of isolated oscillators and the disposition in space. The creation of solitary states through the homoclinic bifurcation is described and the regions of co-existence of obtained states and typical examples of dynamics have been identified. Our analysis suggests that solitary states can be observed in a wide class of networks relevant to various real-world systems.