Short-term Prediction of Hyperchaotic Flow Using Echo State Network

An echo state network with a reservoir consisting of 200 tanh neurons is applied to the short-term prediction of a chaotic time series generated using the augmented Lorenz equations as a hyperchaotic flow model. The predictive performance is examined in terms of the Kolmogorov-Sinai entropy and the Kaplan - Yorke dimension of a chaotic attractor in comparison with those for chaotic flow models having a single positive Lyapunov exponent. We discuss the predictive performance of the reservoir in terms of a universal simulator of chaotic attractors on the basis of Ueda's view of chaos, i.e., random transitions between unstable periodic orbits in a chaotic attractor.