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

Abstract

Understanding the dynamical properties of coupled phase oscillator systems with heterogeneous oscillator frequencies has been a long-standing challenge of complex systems theory. While the seminal work of Ott and Antonsen dramatically improved our theoretical understanding of coupled phase oscillators for a small family of oscillator frequency distributions, we here present a mean-field reduction method for arbitrary frequency distributions. Our method leverages the drastic dimensionality reduction obtained for Lorentzian frequency distributions, and combines it with a data-driven multi-ensemble approach. As such, the method renders the Ott-Antonsen equations directly applicable to empirical distributions of phase oscillator frequencies, often achieving a drastic dimensionality reduction and allowing to study real-world physical and biological systems by means of stability, sensitivity, and bifurcation analyses.