Inverse problems for dynamic patterns in coupled oscillator networks: when larger networks are simpler

Area of Science:

• Complex Systems
• Nonlinear Dynamics
• Statistical Physics

Background:

• Networks of coupled phase oscillators are fundamental models in science and engineering.
• Mean-field approaches analyze dynamics in large oscillator networks, predicting emergent patterns.
• Partially synchronized states in these networks often lead to statistical equilibrium relations.

Purpose of the Study:

• To derive and validate statistical equilibrium relations for partially synchronized states in coupled oscillator networks.
• To demonstrate the method's effectiveness for parameter reconstruction from observable quantities.
• To explore applications in analyzing complex phenomena like chimera states.

Main Methods:

• Utilizing a variant of the mean-field approach for large networks.
• Deriving statistical equilibrium relations linking observable quantities to internal oscillator parameters.
• Assessing the accuracy of these relations for finite-size networks.
• Applying the method to networks exhibiting chimera states with nonlocal coupling.

Main Results:

• Demonstrated derivation of statistical equilibrium relations for partially synchronized patterns.
• Quantified the accuracy of these relations for finite-size networks.
• Showcased the method's efficacy in reconstructing model parameters from time-averaged observables.
• Successfully applied the method to analyze chimera states in nonlocal coupling oscillator networks.

Conclusions:

• The developed method provides a powerful tool for analyzing complex dynamics in large networks of coupled oscillators.
• It is particularly effective for reconstructing parameters from incomplete, noisy, or unevenly sampled data.
• The approach is extendable to various network topologies and coupling schemes, broadening its applicability.