Institution: | a Institute of Automation, University of Bremen, Otto-Hahn-Allee./NW1, D-28359, Bremen, Germany b Department of Electrical Engineering, K. N. Toosi University of Technology, Sayyed Khandan Bridge, P.O. Box 16315-1355, Tehran, Iran c Department of Electrical Engineering, Faculty of Engineering, University of Tehran, North Kargar Avenue, P.O. Box 14395-515, Tehran, Iran |
Abstract: | In this paper, a method for estimating an attractor embedding dimension based on polynomial models and its application in investigating the dimension of Bremen climatic dynamics are presented. The attractor embedding dimension provides the primary knowledge for analyzing the invariant characteristics of the attractor and determines the number of necessary variables to model the dynamics. Therefore, the optimality of this dimension has an important role in computational efforts, analysis of the Lyapunov exponents, and efficiency of modeling and prediction. The smoothness property of the reconstructed map implies that, there is no self-intersection in the reconstructed attractor. The method of this paper relies on testing this property by locally fitting a general polynomial autoregressive model to the given data and evaluating the normalized one step ahead prediction error. The corresponding algorithms are developed in uni/multivariate form and some probable advantages of using information from other time series are discussed. The effectiveness of the proposed method is shown by simulation results of its application to some well-known chaotic benchmark systems. Finally, the proposed methodology is applied to two major dynamic components of the climate data of the Bremen city to estimate the related minimum attractor embedding dimension. |