Quaternionic Multilayer Perceptrons for Chaotic Time Series Prediction

In the paper a new type of Multilayer Perceptron, developed in Quaternion Algebra, is adopted to realize short-time prediction of chaotic time series. The new introduced neural structure, based on MLP and developed in the hypercomplex quaternion algebra (HMLP) allows accurate results with a decreased network complexity with respect to the real MLP. The short term prediction of various chaotic circuits and systems has been performed, with particular emphasys to the Chua's circuit, the Saito's circuit with hyperchaotic behaviour and the Lorenz system. The accuracy of the prediction is evaluated through a correlation index between the actual predicted terms of the time series. A comparison of the performance obtained with both the real MLP and the hypercomplex one is also reported.