# Effects of Janus Oscillators in the Kuramoto Model with Positive and Negative Couplings

## TL;DR

This paper investigates how Janus oscillators influence the dynamics of a Kuramoto model with mixed positive and negative couplings, revealing their role in cluster formation and traveling behavior.

## Contribution

It introduces a numerical and analytical study of Janus oscillators' effects on cluster dynamics and traveling speeds in a mixed-coupling Kuramoto system.

## Key findings

- Janus oscillators can form clusters and affect system synchronization.
- The traveling speed of clusters depends on coupling parameters and oscillator fractions.
- An analytical expression accurately predicts the traveling speed based on system parameters.

## Abstract

We study the effects of Janus oscillators in a system of phase oscillators in which the coupling constants take both positive and negative values. Janus oscillators may also form a cluster when the other ones are ordered and we calculate numerically the traveling speed of three clusters emerging in the system and average separations between them as well as the order parameters for three groups of oscillators, as the coupling constants and the fractions of positive and Janus oscillators are varied. An expression explaining the dependence of the traveling speed on these parameters is obtained and observed to fit well the numerical data. With the help of this, we describe how Janus oscillators affect the traveling of the clusters in the system.