Model equations from a chaotic time series

Agarwal, A. K. ; Ahalpara, D. P. ; Kaw, P. K. ; Prabhakara, H. R. ; Sen, A. (1990) Model equations from a chaotic time series Pramana - Journal of Physics, 35 (3). pp. 287-301. ISSN 0304-4289

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We present a method for obtaining a set of dynamical equations for a system that exhibits a chaotic time series. The time series data is first embedded in an appropriate phase space by using the improved time delay technique of Broomhead and King (1986). Next, assuming that the flow in this space is governed by a set of coupled first order nonlinear ordinary differential equations, a least squares fitting method is employed to derive values for the various unknown coefficients. The ability of the resulting model equations to reproduce global properties like the geometry of the attractor and Lyapunov exponents is demonstrated by treating the numerical solution of a single variable of the Lorenz and Rossler systems in the chaotic regime as the test time series. The equations are found to provide good short term prediction (a few cycle times) but display large errors over large prediction time. The source of this shortcoming and some possible improvements are discussed.

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:Time Series; Chaos; Model Equations; Strange Attractor
ID Code:25138
Deposited On:01 Dec 2010 12:04
Last Modified:17 May 2016 08:39

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