Modelling of chaotic systems based on modified weighted recurrent least squares support vector machines

Abstract

Positive Lyapunov exponents cause the errors in modelling of the chaotic time series to grow exponentially. In this paper, we propose the modified version of the support vector machines (SVM) to deal with this problem. Based on recurrent least squares support vector machines (RLS-SVM), we introduce a weighted term to the cost function to compensate the prediction errors resulting from the positive global Lyapunov exponents. To demonstrate the effectiveness of our algorithm, we use the power spectrum and dynamic invariants involving the Lyapunov exponents and the correlation dimension as criterions and then apply our method to the Santa Fe competition time series. The simulation results shows that the proposed method can capture the dynamics of the chaotic time series effectively.