Short-term forecasting of hyperchaotic time series by noisy echo state network

We have applied a noisy echo state network, wherein pseudorandom numbers subject to uniform distribution are input to the reservoir nodes, to the short-term forecasting of a hyperchaotic time series generated by a star network of nonidentical Lorenz subsystems. The chaotic dynamics have five positive Lyapunov exponents with a Lyapunov dimension exceeding 12. Although the predictive model incurs a large prediction error, it is capable of reproducing the geometric structure of the hyperchaotic attractor with sufficient fidelity. We discuss these results in terms of Ueda’s view of chaos, wherein chaotic dynamical behavior is recognized as a piecewise deterministic process with intervening stochastic processes such as numerical round-off errors and perturbations caused by experimental measurements.