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

Richard Gast; Shotaro Takasu; Helmut Schmidt; Ann Kennedy

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arXiv · 2607.09516

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

Richard Gast·Shotaro Takasu·Helmut Schmidt·Ann Kennedy

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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.

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Richard Gast, Shotaro Takasu, Helmut Schmidt, Ann Kennedy. 2026-07-10. A multi-ensemble mean-field reduction method for networks of globally coupled phase oscillators with arbitrary parameter distributions. https://arxiv.org/abs/2607.09516

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