Linked and knotted chimera filaments in oscillatory systems

TL;DR

This paper provides numerical evidence that stable knotted and linked vortex structures, including scroll wave chimeras, can exist in oscillatory systems with intermediate-range coupling, revealing new topological superstructures.

Contribution

It demonstrates the existence of stable knotted and linked vortex filaments in oscillatory systems with nonlocal coupling, a phenomenon previously unobserved in such systems.

Findings

Stable knots and links exist in oscillatory systems with intermediate coupling.

Vortex lines correspond to scroll wave chimeras, showing spontaneous synchrony breaking.

Complex systems exhibit topological superstructures combining knotted filaments and defect sheets.

Abstract

While the existence of stable knotted and linked vortex lines has been established in many experimental and theoretical systems, their existence in oscillatory systems and systems with nonlocal coupling has remained elusive. Here, we present strong numerical evidence that stable knots and links such as trefoils and Hopf links do exist in simple, complex, and chaotic oscillatory systems if the coupling between the oscillators is neither too short ranged nor too long ranged. In this case, effective repulsive forces between vortex lines in knotted and linked structures stabilize curvature-driven shrinkage observed for single vortex rings. In contrast to real fluids and excitable media, the vortex lines correspond to scroll wave chimeras [synchronized scroll waves with spatially extended (tubelike) unsynchronized filaments], a prime example of spontaneous synchrony breaking in systems of identical oscillators. In the case of complex oscillatory systems, this leads to a novel topological superstructure combining knotted filaments and synchronization defect sheets.