A laminar chaotic saddle within a turbulent attractor

TL;DR

This paper identifies a chaotic saddle within a turbulent attractor, explaining intermittent laminar and bursty states in high-dimensional chaotic systems like fluid turbulence, and shows these saddles persist across parameters.

Contribution

It introduces the concept of a chaotic saddle as the skeleton of laminar states within turbulent attractors, advancing understanding of intermittency in high-dimensional chaos.

Findings

Chaotic saddles underlie intermittency in turbulence.

Chaotic saddles persist over a wide parameter range.

Phase synchronization occurs in the turbulent model.

Abstract

Intermittent switchings between weakly chaotic (laminar) and strongly chaotic (bursty) states are often observed in systems with high-dimensional chaotic attractors, such as fluid turbulence. They differ from the intermittency of a low-dimensional system accompanied by the stability change of a fixed point or a periodic orbit in that the intermittency of a high-dimensional system tends to appear in a wide range of parameters. This paper considers a case where the skeleton of a laminar state $L$ exists as a proper chaotic subset $S$ of a chaotic attractor $X$, that is, $S\ \subsetneq\ X$. We characterize such a laminar state $L$ by a chaotic saddle $S$, which is densely filled with periodic orbits of different numbers of unstable directions. This study demonstrates the presence of chaotic saddles underlying intermittency in fluid turbulence and phase synchronization. Furthermore, we confirm that chaotic saddles persist for a wide range of parameters. Also, a kind of phase synchronization turns out to occur in the turbulent model.