Detection of Generalized Synchronization using Echo State Networks

Abstract: Generalized synchronization between coupled dynamical systems is a phenomenon of relevance in applications that range from secure communications to physiological modelling. Here we test the capabilities of reservoir computing and, in particular, echo state networks for the detection of generalized synchronization. A nonlinear dynamical system consisting of two coupled R\"ossler chaotic attractors is used to generate temporal series consisting of time-locked generalized synchronized sequences interleaved by unsynchronized ones. Correctly tuned, echo state networks are able to efficiently discriminate between unsynchronized and synchronized sequences. Compared to other state-of-the-art techniques of synchronization detection, the online capabilities of the proposed ESN based methodology make it a promising choice for real-time applications aiming to monitor dynamical synchronization changes in continuous signals.