On the dynamics of traveling phase-oscillators with positive and negative couplings

TL;DR

This paper numerically studies the dynamics of traveling clusters in phase oscillators with mixed positive and negative couplings, analyzing how parameters influence traveling speed, phase distribution, and order parameters.

Contribution

It provides a detailed numerical analysis of traveling states in coupled oscillators with mixed couplings, including conditions for their emergence.

Findings

Traveling speed depends on coupling ratio and fraction of positive oscillators.

Phase distribution and cluster separation vary with system parameters.

Conditions for traveling states are identified with and without periodic driving.

Abstract

We investigate numerically the dynamics of traveling clusters in systems of phase oscillators, some of which possess positive couplings and others negative couplings. The phase distribution, speed of traveling, and average separation between clusters as well as order parameters for positive and negative oscillators are computed, as the ratio of the two coupling constants and/or the fraction of positive oscillators are varied. The traveling speed depending on these parameters is obtained and observed to fit well with the numerical data of the systems. With the help of this, we describe the conditions for the traveling state to appear in the systems with or without periodic driving.