Time-lagged recurrence: A data-driven method to estimate the predictability of dynamical systems.

Area of Science:

• Complex Systems Science
• Nonlinear Dynamics
• Atmospheric Science

Background:

• Nonlinear dynamical systems are prevalent but difficult to forecast due to sensitivity to initial conditions and multi-scale processes.
• Traditional methods like Lyapunov spectrum analysis require knowledge of the dynamic forward operator, which is often unknown or poorly represented by noisy data.

Purpose of the Study:

• To propose a data-driven method for analyzing the local predictability of dynamical systems.
• To demonstrate the effectiveness of a recurrence-based approach for estimating local predictability.
• To explore the scale-dependent nature of predictability and its relationship with information theory.

Main Methods:

• A data-driven approach based on the concept of recurrence.
• Application to idealized systems and real-world atmospheric field datasets.
• Analysis of the method's relationship with local dynamical indices and information theory.

Main Results:

• The proposed method effectively estimates local predictability in both idealized and real-world complex systems.
• The approach reveals the scale-dependent nature of predictability.
• Demonstrated potential for real-time application and diagnostic use in complex systems.

Conclusions:

• The recurrence-based method offers a powerful tool for analyzing local predictability in nonlinear dynamical systems.
• It overcomes limitations of traditional methods by not requiring knowledge of the dynamic forward operator.
• The approach provides insights into scale-dependent predictability and has broad applications in complex system analysis.