Network inference from oscillatory signals based on circle map

To understand and control the dynamics of coupled oscillators, it is important to reveal the structure of the interaction network from observed data. While various techniques have been developed for inferring the network of asynchronous systems, it remains challenging to infer the network of synchronized oscillators without external stimulations. In this study, we develop a method for non-invasively inferring the network of synchronized and/or de-synchronized oscillators. An approach to network inference would be to fit the data to a set of differential equations describing the dynamics of phase oscillators. However, we show that this method fails to infer the true network due to the problems that arise when we use short-time phase differences. Therefore, we propose a method based on the circle map, which describes the phase change in one oscillatory cycle. We demonstrate the efficacy of the proposed method through the successful inference of the network structure from simulated data of limit cycle oscillator models. Our method provides a unified and concise framework for network estimation for a wide class of oscillator systems.