Detecting unstable periodic orbits based only on time series: When adaptive delayed feedback control meets reservoir...

Area of Science:

• Nonlinear Dynamics
• Machine Learning
• Control Theory

Background:

• Detecting unstable periodic orbits (UPOs) is crucial for understanding nonlinear dynamical systems.
• Traditional methods often require a priori knowledge of the system's explicit model, limiting their applicability.
• Data-driven and model-free approaches are needed for systems where the model is unknown.

Purpose of the Study:

• To develop and demonstrate a novel data-driven, model-free method for detecting and controlling UPOs.
• To integrate reservoir computing with adaptive delayed feedback control for this purpose.
• To analyze the influence of reservoir computing configurations on UPO detection accuracy.

Main Methods:

• Utilized reservoir computing, a machine learning technique, for system learning and prediction.
• Employed adaptive delayed feedback control, a nonlinear control strategy.
• Combined these methods to create a data-driven approach for UPO detection in unknown systems.

Main Results:

• Successfully detected and controlled UPOs in representative nonlinear dynamical systems using the proposed method.
• Demonstrated the effectiveness of the combined reservoir computing and adaptive delayed feedback control approach.
• Showcased how reservoir computing configurations impact UPO detection accuracy.

Conclusions:

• The proposed data-driven, model-free method effectively detects and controls UPOs in unknown nonlinear systems.
• Reservoir computing shows significant potential for dynamical systems learning and prediction, particularly in synchronization contexts.
• The method offers a powerful tool for analyzing complex nonlinear dynamics without prior model information.