Developing reservoir computing models for anticipatory synchronization with chaotic time series and real-time prediction.

Abstract

We show that combining the ideas of anticipatory synchronization and machine learning enables real-time prediction of chaotic time series without prior knowledge of the system model. A next-generation reservoir computing approach is used to develop slave system models for anticipatory synchronization with scalar chaotic time series. The multidimensional state space is reconstructed using time-delay embedding coordinates. The developed models satisfy the requirement of the negativeness of the largest transversal Lyapunov exponent, which is necessary for the stability of the anticipatory synchronization mode. The prediction time of one slave system constructed in this way is equal to the embedding delay time. We increase the prediction time by implementing a chain of serially connected slave systems. The prediction performance using anticipatory synchronization and machine learning is demonstrated for scalar chaotic time series obtained from Rössler and Lorenz systems, as well as for experimental time series of an electronic chaos oscillator and a theoretical time series generated by a large heterogeneous network of quadratic integrate-and-fire neurons.