Modelling of Chaotic Systems with Novel Weighted Recurrent Least Squares Support Vector Machines

Abstract

This paper discusses the use of Support Vector Machines(SVM) for dynamic modelling of the chaotic time series. Based on Recurrent Least Squares Support Vector Machines (RLS-SVM), a weighted term is introduced to the cost function to compensate the prediction errors resulting from the positive global Lyapunov exponent in context of the chaotic time series. For demonstrating the effectiveness of our algorithm, the dynamic invariants involves the Lyapunov exponent and the correlation dimension are used for criterions. Finally we apply our method to Santa Fe competition time series. The simulation results shows that the proposed method can capture the dynamics of the chaotic time series effectively.