Modelling of Chaotic Systems with Recurrent Least Squares Support Vector Machines Combined with Reconstructed Embedding Phase Space

• Published in: Advances in Natural Computation pp. 573 - 581
• Main Authors: Xiang, Zheng, Zhang, Taiyi, Sun, Jiancheng
• Format: Book Chapter Conference Proceeding
• Language: English
• Published: Berlin, Heidelberg Springer Berlin Heidelberg 2005; Springer
• Series: Lecture Notes in Computer Science
• Subjects: Applied sciences; Artificial intelligence; Chaotic System; Computer science; control theory; systems; Correlation Dimension; Exact sciences and technology; Lyapunov Exponent; Strange Attractor; Support Vector Machine; Chaos; Invariant; Recurrence; Statistical analysis; Correlation dimension; Time series; Modeling; Least squares method; Lyapunov exponent; Vector support machine; Dynamic model; Phase space; Power spectrum
• ISBN: 3540283234; 9783540283232
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/11539087_73

A new strategy of modelling of chaotic systems is presented. First, more information is acquired utilizing the reconstructed embedding phase space. Then, based on the Recurrent Least Squares Support Vector Machines (RLS-SVM), modelling of the chaotic system is realized. 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 Chua‘s circuit time series. The simulation of dynamic invariants between the origin and generated time series shows that the proposed method can capture the dynamics of the chaotic time series effectively.