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

This study investigates inference of the coupling strength and the
frequency distribution in a coupled Stuart-Landau oscillator system,
which is a paradigmatic model of coupled limit-cycle oscillators. We
analyze the system using phase-amplitude reduction, which yields both
phase and amplitude equations under external forces. The amplitude
equation　focuses on describing deviations from the limit cycle, which
are utilized to infer the coupling strength from microscopic
observation of time series of selected oscillators. Meanwhile, the
phase equation is essential for applying a linear response theory to
infer the frequency distribution from system's macroscopic
responses. In the proposed method, it is sufficient to observe only
one variable among the two variables consisting of a Stuart-Landau
oscillator. Through numerical simulations, we demonstrate
effectiveness of this approach in inferring the key parameters. Our
method offers a robust framework for inferring coupled limit-cycle
oscillator systems and has potential applications in a wide range of
fields.