An Algorithm for Estimating Fixed Points of Dynamical Systems from Time Series-Reference-Cited by-同舟云学术

An Algorithm for Estimating Fixed Points of Dynamical Systems from Time Series

Published:1998-11 Issue:11 Volume:08 Page:2203-2213
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

Aguirre Luis A.¹²,Souza Álvaro V. P.¹

Affiliation:

1. Centro de Pesquisa e Desenvolvimento em Engenharia Elétrica, Universidade Federal de Minas Gerais, Av. Antônio Carlos 6627, 31270-901 Belo Horizonte, M.G., Brazil

2. Departamento de Engenharia Electrônica, Universidade Federal de Minas Gerais, Av. Antônio Carlos 6627, 31270-901 Belo Horizonte, M.G., Brazil

Abstract

This paper presents an algorithm for estimating fixed points of dynamical systems from time series. In some cases the new procedure can accurately estimate fixed points of which there is very little information in the data. Another advantage is that, although no prior knowledge is assumed, the new algorithm permits the user to employ a priori information about the system such as symmetry and the existence of a trivial fixed point. The new algorithm is tested on the Lorenz and Rössler systems and on real data taken from Chua's circuit.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127498001790

Reference11 articles.

1. A nonlinear correlation function for selecting the delay time in dynamical reconstructions

2. Improved structure selection for nonlinear models based on term clustering

3. GLOBAL NONLINEAR POLYNOMIAL MODELS: STRUCTURE, TERM CLUSTERS AND FIXED POINTS

4. Nonlinear Identification and Cluster Analysis of Chaotic Attractors from a Real Implementation of Chua's Circuit

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