Controlling unstable chaos: stabilizing chimera states by feedback

Area of Science:

• Complex Systems
• Nonlinear Dynamics
• Statistical Physics

Background:

• Chaotic systems often exhibit unstable regimes that are difficult to study.
• Chimera states represent unique coherence-incoherence patterns in coupled oscillator systems.
• Tracking chaotic attractors through bifurcations is crucial for understanding system dynamics.

Purpose of the Study:

• To present a novel control scheme for stabilizing unstable chaotic regimes.
• To enable tracking of high-dimensional chaotic attractors through bifurcations.
• To demonstrate the scheme's applicability to chimera states in coupled oscillator systems.

Main Methods:

• A noninvasive control scheme inspired by delayed feedback control.
• Treating chaotic regimes as statistical equilibria with finite-size fluctuations.
• Applying the control to coupled oscillator systems exhibiting chimera states.

Main Results:

• The control scheme successfully finds and stabilizes unstable chaotic regimes.
• High-dimensional chaotic attractors can be tracked through bifurcations.
• Chimera states are made observable near coherence, with fewer oscillators and random initial conditions.

Conclusions:

• The presented control scheme offers a new method for studying complex chaotic dynamics.
• This approach facilitates the observation and analysis of phenomena like chimera states.
• The noninvasive nature of the control, in a relaxed sense, broadens its applicability.