Chaotic time series prediction via quaternionic multilayer perceptrons

In the paper a new type of multilayer perceptron, developed in quaternion algebra (QMLP), is adopted in order to predict chaotic time series. The use of QMLPs allows to perform accurate time series prediction with a decreased network complexity with respect to the classical real valued MLP, when the involved time series are multidimensional. The approach proposed has been adopted to estimate the chaotic behavior of Chua's circuit and of a circuit containing a piece-wise linear hysteresis element. A comparison between the performance of the QMLP and the real MLP is also reported in order to show the improvement introduced by the QMLP in terms of a decreasing of the network complexity.