A multi-ensemble mean-field reduction method for networks of globally coupled phase oscillators with arbitrary...

Area of Science:

• Complex Systems Theory
• Nonlinear Dynamics
• Statistical Physics

Background:

• Analyzing coupled phase oscillator systems with heterogeneous frequencies is a key challenge in complex systems.
• The Ott-Antonsen theory provides insights but is limited to specific frequency distributions.

Purpose of the Study:

• To develop a generalized mean-field reduction method applicable to arbitrary frequency distributions.
• To extend the applicability of the Ott-Antonsen framework to empirical data.

Main Methods:

• A novel mean-field reduction technique is presented.
• The method utilizes dimensionality reduction strategies from Lorentzian distributions.
• A data-driven multi-ensemble approach is integrated.

Main Results:

• The developed method successfully applies the Ott-Antonsen equations to arbitrary frequency distributions.
• Significant dimensionality reduction is achieved for empirical oscillator frequency distributions.
• The approach facilitates stability, sensitivity, and bifurcation analyses.

Conclusions:

• This work provides a powerful tool for understanding complex systems with heterogeneous oscillators.
• The method bridges theoretical models with real-world physical and biological systems.
• It opens new avenues for analyzing emergent dynamics in diverse scientific fields.