Neural networks for nonlinear mutual prediction of coupled chaotic time series

Multilayer perceptrons (MLP) were trained to mutually predict nonlinearly coupled identical Henon systems. Several combinations of input and target time series were presented to networks of different structure during training. After presenting the trained networks with a short segment of Henon data they were able to generate Henon time series of variable duration. This was verified by comparing the attractors of the training set and the generated data. Furthermore, the performance of mutual prediction of data outside the training set was found to be dependent on the strength of coupling among the chaotic time series and on their similarities regarding their generation equations. The method was also applied to univariate and multivariate ECoG data. The motivation of this work is to predict and analyse the development of epileptic seizures by searching for recurring nonlinear dependencies and similarities in multivariate ECoG recordings.