# Collective dynamics of random Janus oscillator networks

## TL;DR

This paper investigates the collective behavior of Janus oscillators on various large networks, revealing persistent complex dynamics, coexistence of states, and abrupt transitions, with unique features in scale-free networks.

## Contribution

It demonstrates that Janus oscillator dynamics persist in large random networks and uncovers novel phenomena like state coexistence and abrupt transitions across different topologies.

## Key findings

- Rich dynamics persist in large networks.
- Coexistence of synchronized and oscillatory states.
- Abrupt transitions in order parameters.

## Abstract

Janus oscillators have been recently introduced as a remarkably simple phase oscillator model that exhibits non-trivial dynamical patterns -- such as chimeras, explosive transitions, and asymmetry-induced synchronization -- that once were only observed in specifically tailored models. Here we study ensembles of Janus oscillators coupled on large homogeneous and heterogeneous networks. By virtue of the Ott-Antonsen reduction scheme, we find that the rich dynamics of Janus oscillators persists in the thermodynamic limit of random regular, Erd\H{o}s-R\'enyi and scale-free random networks. We uncover for all these networks the coexistence between partially synchronized state and a multitude of states displaying global oscillations. Furthermore, abrupt transitions of the global and local order parameters are observed for all topologies considered. Interestingly, only for scale-free networks, it is found that states displaying global oscillations vanish in the thermodynamic limit.