{"ID":6497634,"CreatedAt":"2026-07-13T01:19:40.13847098Z","UpdatedAt":"2026-07-14T01:36:59.12045529Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.09516","arxiv_id":"2607.09516","title":"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.","short_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 famil...","url_abs":"https://arxiv.org/abs/2607.09516","url_pdf":"https://arxiv.org/pdf/2607.09516v1","authors":"[\"Richard Gast\",\"Shotaro Takasu\",\"Helmut Schmidt\",\"Ann Kennedy\"]","published":"2026-07-10T15:27:57Z","proceeding":"cond-mat.dis-nn","tasks":"[\"cond-mat.dis-nn\",\"nlin.CD\",\"q-bio.NC\"]","methods":"[]","has_code":false}