Discordant synchronization patterns on directed networks of identical phase oscillators with attractive and repulsive couplings

TL;DR

This paper investigates the complex collective behaviors of identical phase oscillators on directed networks with mixed attractive and repulsive couplings, revealing various synchronized states, bistability, and chimera-like phenomena.

Contribution

It introduces a framework combining asymmetric interactions and the Ott-Antonsen theory to analyze novel synchronization patterns in directed oscillator networks.

Findings

Existence of traveling-wave and π-states.

Bistability among multiple collective states.

Detection of chimera-like states not captured by OA theory.

Abstract

We study the collective dynamics of identical phase oscillators on globally coupled networks whose interactions are asymmetric and mediated by positive and negative couplings. We split the set of oscillators into two interconnected subpopulations. In this setup, oscillators belonging to the same group interact via symmetric couplings while the interaction between subpopulations occurs in an asymmetric fashion. By employing the dimensional reduction scheme of the Ott-Antonsen (OA) theory, we verify the existence of traveling-wave and $\pi$-states, in addition to the classical fully synchronized and incoherent states. Bistability between all collective states is reported. Analytical results are generally in excellent agreement with simulations; for some parameters and initial conditions, however, we numerically detect chimera-like states which are not captured by the OA theory.