Inferring coupling strength and natural frequency distribution in coupled Stuart-Landau oscillators using linear response

TL;DR

This paper introduces a method to infer coupling strength and natural frequency distribution in large populations of Stuart-Landau oscillators using minimal linear response observations.

Contribution

It presents a novel inference framework that utilizes linear response data from a single oscillator and macroscopic responses, requiring only one-dimensional observations.

Findings

The method accurately infers coupling strength from oscillator response.

The natural frequency distribution is deduced from macroscopic responses.

Numerical simulations validate the inference approach.

Abstract

We propose a framework to infer the coupling strength and the natural frequency distribution in a coupled Stuart-Landau oscillator system with a large population. The inference method uses observation of linear response of a macroscopic quantity and of an oscillator. We first solve the direct problem on the response with transforming the system into the phase-amplitude equations. Solving the inverse problem, we show that the coupling strength is inferred from observation of an oscillator and the natural frequency distribution from macroscopic responses. The proposed method requires only one-dimensional observation in the two-dimensional Stuart-Landau system. Validity of the inference theory is examined by numerical simulations.