AI 中文总结
针对耦合相位振荡器系统动力学特性研究的挑战，提出一种多系综平均场约化方法，利用洛伦兹频率分布降维并结合数据驱动方法，使Ott-Antonsen方程适用于任意频率分布，可降维并用于分析现实系统。
AI 中文摘要
理解具有异质振荡器频率的耦合相位振荡器系统的动力学特性一直是复杂系统理论的长期挑战。虽然Ott和Antonsen的开创性工作极大地增进了我们对一小类振荡器频率分布的耦合相位振荡器的理论理解，但本文提出了一种适用于任意频率分布的平均场约化方法。该方法利用了洛伦兹频率分布所实现的大幅降维，并将其与数据驱动的多系综方法相结合。这使得Ott-Antonsen方程可直接应用于相位振荡器频率的经验分布，常能实现大幅降维，并可通过稳定性、敏感性和分岔分析来研究现实世界的物理和生物系统。
英文摘要
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.
