Laminar chaotic saddle within a turbulent attractor

Area of Science:

• Complex Systems Dynamics
• Nonlinear Physics
• Fluid Turbulence

Background:

• Intermittent switching between laminar and bursty states is common in high-dimensional chaotic systems, notably fluid turbulence.
• This phenomenon differs from low-dimensional intermittency, often appearing across broad parameter ranges in complex systems.

Purpose of the Study:

• To investigate the role of chaotic saddles in high-dimensional intermittency.
• To characterize laminar states within chaotic attractors using chaotic saddle structures.
• To demonstrate the presence and persistence of chaotic saddles in fluid turbulence and phase synchronization.

Main Methods:

• Characterization of laminar states (L) as chaotic subsets (S) of chaotic attractors (X), denoted S ⊊ X.
• Analysis of chaotic saddles, defined as sets densely filled with periodic orbits possessing varying unstable directions.
• Modeling and simulation of turbulent systems to identify underlying chaotic saddle dynamics.

Main Results:

• The study demonstrates that chaotic saddles underlie intermittency in fluid turbulence and phase synchronization phenomena.
• Chaotic saddles were confirmed to persist across a wide range of system parameters.
• A form of phase synchronization was observed to occur within the turbulent model studied.

Conclusions:

• Chaotic saddles provide a robust framework for understanding intermittency in high-dimensional chaotic systems.
• The persistence of chaotic saddles explains the wide parameter range over which intermittency is observed.
• The findings link chaotic saddle dynamics to phenomena like phase synchronization in turbulent systems.