Dynamic reconstruction of chaotic systems from inter-spike intervals using least squares support vector machines

2006 ◽  
Vol 216 (2) ◽  
pp. 282-293 ◽  
Author(s):  
Serdar Iplikci
Keyword(s):  
Support Vector Machines ◽  
Least Squares ◽  
Chaotic Systems ◽  
Support Vector ◽  
Dynamic Reconstruction ◽  
Vector Machines

MODELING OF CHAOTIC SYSTEMS WITH MULTIWAVELET TRANSFORM COMBINED WITH RECURRENT LEAST SQUARES SUPPORT VECTOR MACHINES

2007 ◽  
Vol 05 (01) ◽  
pp. 1-13
Author(s):  
ZHENG XIANG ◽  
TAIYI ZHANG ◽  
JIANCHENG SUN
Keyword(s):  
Time Series ◽  
Support Vector Machines ◽  
Least Squares ◽  
Chaotic Systems ◽  
Support Vector ◽  
Vector Machines ◽  
Temporal Structures ◽  
Multiwavelet Transform ◽  
Original Time ◽  
Dynamic Invariants

A new algorithm for modeling of chaotic systems is presented in this paper. First, more information is acquired utilizing the reconstructed embedding phase space, and the multiwavelets transform provides a sensible decomposition of the data so that the underlying temporal structures of the original time series become more tractable. Second, based on the Recurrent Least Squares Support Vector Machines (RLS-SVM), modeling of the chaotic system is realized. 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 Chua's circuit time series. The similarity of dynamic invariants between the original and generated time series shows that the proposed method can capture the dynamics of the chaotic time series more effectively.

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