Detecting connectivity of small, dense oscillator networks from dynamical measurements based on a phase modeling approach

An approach is presented for detecting the connectivity between the oscillator elements from the measured multivariate time series data. Our methodology is based upon the phase equation modeling of the oscillator networks, where not only the connection matrix but also the natural frequencies and the interaction function of the oscillators are estimated. Application of this technique to simulated data as well as experimental ones from electrochemical oscillators shows its capability for precise detection of defects in the connection matrix for small-size networks. Dependence of the methodology on the observational noise, the network size, the number of defects, and the data length is also examined.