Estimating Phase Equations from Multivariate Time Series
A novel approach is presented for extracting phase equations from multivariate time series data recorded from a network of weakly coupled limit cycle oscillators. Our aim is to estimate all the important properties of the phase equations such as natural frequencies and interaction function between the oscillators. Our approach requires the measurement of an experimental observable of the oscillators; in contrast to previous methods, it does not require measurements in isolated single, or two-oscillator setups. This non-invasive technique should be advantageous in biological systems, where extraction of few oscillators may be a difficult task. The method is most efficient when data is taken from the non-synchronized regime where the phases of the oscillators are affected by coupling but where no complete phase locking of the oscillators occurs. Applicability to experimental systems is demonstrated by using a network of electrochemical oscillators; the experimentally obtained phase model is used to predict the synchronization diagram of the system.