Method of calculating Lyapunov exponents for time series using artificial neural networks committees

The aim of this work is to develop a method for calculating all Lyapunov exponents from time series with high accuracy. To achieve this goal we propose a new method for determining the local and global Lyapunov exponents for a given time series. A special feature of the proposed method is the use of neural networks committee for the approximation of a dynamical system, generating the time series. Approximation model of a dynamicalal system is a trained neural network. The committees of neural networks are used to improve the accuracy of calculation of local and global Lyapunov exponents. In order to test the proposed method, we used time series that have been generated by the chaotic logistic map, Henon map and the X-component of the Lorenz system. As a result of numerical experiments we have shown that for the model time series the proposed method determines all the Lyapunov exponents of listed above dynamical systems with good accuracy. We have also considered the examples of real world time series such as financial examples and electroencephalogram examples.