Control of chaotic Taylor-Couette flow with time-delayed feedback

Area of Science:

• Fluid Dynamics
• Nonlinear Dynamics
• Chaos Theory

Background:

• Taylor-Couette flow exhibits complex chaotic attractors.
• Unstable periodic orbits are key to understanding chaotic systems.
• Controlling chaos is crucial for various scientific and engineering applications.

Purpose of the Study:

• To stabilize unstable periodic orbits within the chaotic Taylor-Couette flow.
• To apply a time-delay autosynchronization algorithm for chaos control.
• To experimentally determine optimal feedback parameters and their dependence on control parameters.

Main Methods:

• Utilizing a time-delay autosynchronization algorithm.
• Implementing the algorithm on an experimental chaotic attractor.
• Systematically varying control parameters to observe effects on stabilization.

Main Results:

• Successful stabilization of previously unstable periodic orbits.
• Identification of optimal feedback parameters for the autosynchronization algorithm.
• Demonstration of the dependence of optimal parameters on the main control parameter.

Conclusions:

• Time-delay autosynchronization is an effective method for controlling chaos in Taylor-Couette flow.
• The study provides experimentally validated parameters for chaos control.
• This approach offers a pathway for manipulating complex fluid behaviors.