Approximating discrete mapping of chaotic dynamical system based on on-line EM algorithm

Discusses the reconstruction of chaotic dynamics by using a normalized Gaussian network (NGnet). The NGnet is trained by an online expectation maximization (EM) algorithm in order to learn the discrete mapping of the chaotic dynamics. We also investigate the robustness of our approach to two kinds of noise processes: system noise and observation noise. It is shown that a trained NGnet is able to reproduce a chaotic attractor, even under various noise conditions. The trained NGnet also shows good prediction performance. When only part of the dynamical variables are observed, the NGnet is trained to learn the discrete mapping in the delay coordinate space. It is shown that the chaotic dynamics is able to be learned with this method under the two kinds of noise.