Importance-sampling computation of statistical properties of coupled oscillators

Area of Science:

• Physics
• Computational Science
• Statistical Mechanics

Background:

• Globally coupled oscillators are fundamental to understanding synchronization phenomena.
• Studying rare dynamical states in large systems is computationally challenging.

Purpose of the Study:

• To introduce an efficient importance-sampling Monte Carlo algorithm for analyzing rare events in globally coupled oscillator systems.
• To investigate the distribution of dynamical trajectory measures in large-scale oscillator networks.

Main Methods:

• Implementation of an importance-sampling Monte Carlo algorithm.
• Application to the driven-dissipative Kuramoto model (synchronization) and the conservative Hamiltonian mean-field model (long-range interactions).
• Analysis of distributions for finite-time Lyapunov exponent and time-averaged order parameter.

Main Results:

• The computational method effectively estimates tails of distributions for low-probability states.
• Distributions show vanishing standard deviation but increasing skewness with the number of oscillators.
• Nontrivial asymmetries and rare states persist in large oscillator systems.

Conclusions:

• The developed algorithm provides efficient analysis of rare dynamical states in complex oscillator systems.
• Large numbers of oscillators do not eliminate persistent asymmetries or the occurrence of atypical system behaviors.
• Findings are relevant for diverse fields employing coupled oscillator models, from physics to neuroscience.