Traveling phase waves in asymmetric networks of noisy chaotic attractors

TL;DR

This paper investigates traveling phase waves in asymmetric networks of noisy chaotic R"ossler oscillators, revealing coexistence of synchronized phase patterns with chaotic amplitude dynamics and connecting these phenomena to the Kuramoto model.

Contribution

It introduces the concept of traveling phase waves in asymmetric noisy chaotic networks and links these dynamics to established phase-coupling models.

Findings

Traveling phase waves emerge in asymmetric noisy R"ossler networks.

Coexistence of synchronized phase dynamics with chaotic amplitudes is observed.

Connections between chaotic oscillator dynamics and the Kuramoto model are established.

Abstract

We explore identical R\"ossler systems organized into two equally-sized groups, among which differing positive and negative in- and out-coupling strengths are allowed. Patterns of distinctly synchronized phase dynamics are observed, which coexist with chaotically evolving amplitudes. In particular, we report the emergence of traveling phase waves, i.e. states in which the oscillators settle on a new rhythm different from their own. We further elucidate our findings through phase-coupled R\"ossler systems, establishing a connection with the Kuramoto model. Together with the study of noise effects, our results suggest a promising new avenue towards the coexistence of chaotic, noisy and regular collective dynamics.