Collective dynamics in two populations of noisy oscillators with asymmetric interactions

TL;DR

This paper investigates the complex collective behaviors of two interconnected populations of noisy oscillators with asymmetric interactions, revealing novel patterns like phase discordance, traveling waves, and bistability through analytical and bifurcation analysis.

Contribution

It introduces a minimal model of two coupled oscillator networks with asymmetric in- and out-coupling, uncovering new dynamical states and bifurcation phenomena.

Findings

Discovery of phase discordance with constant phase lag

Emergence of traveling wave solutions from phase differences

Existence of bistability between different collective states

Abstract

We study two intertwined globally coupled networks of noisy Kuramoto phase oscillators that have the same natural frequency, but differ in their perception of the mean field and their contribution to it. Such a give-and-take mechanism is given by asymmetric in- and out-coupling strengths which can be both positive and negative. We uncover in this minimal network of networks intriguing patterns of discordance, where the ensemble splits into two clusters separated by a constant phase lag. If it differs from $\pi$, then traveling wave solutions emerge. We observe a second route to traveling waves via traditional one-cluster states. Bistability is found between the various collective states. Analytical results and bifurcation diagrams are derived with a reduced system.