Phase Space Reconstruction of Chaotic Time Series Using an Intelligent Method

Subject Areas : Renewable energy

Maryam  Pari Zangeneh ¹ (Msc/Islamic Azad University, Najaf Abad Branch)
Mohammad  Ataei ² (Associate Professor/Isfahan University)
Peiman  Moallem ³ (Assistant Professor/Isfahan University)

Received: 2010-03-11 Accepted : 2010-08-16 Published : 2010-11-01

Keywords: Embedding dimension, False nearest neighbors, Chaotic time series, Focused time delay neural network,

Abstract :

 In the face of a chaotic system whose mathematical model is not available, because of unknown effective factors and unavailable dynamical equations, using time series approach can be useful. Therefore, phase space reconstruction of a chaotic system by using a scalar time series from its output observations is considered for obtaining information on this system from its one-dimensional signal. Two parameters Delay time and Embedding dimension are needed for phase space reconstruction based on embedding theorem.  In this paper a method for estimation of an appropriate embedding dimension of underlying chaotic system from the observed time series by using Time Delay Neural Network (TDNN) is presented. This new way is different from the conventional False Nearest Neighbors (FNN) method. The embedding dimension estimations have been compared with FNN method and their comparison shows the effectiveness of the proposed methodology.