A numerical estimate of the regularity of a family of Strange Non-Chaotic Attractors

Lluís Alsedà i Soler; David Romero i Sànchez; Jose M. Mondelo Gonzalez

doi:https://doi.org/10.1016/j.physd.2016.12.006

A numerical estimate of the regularity of a family of Strange Non-Chaotic Attractors

Lluís Alsedà i Soler, David Romero i Sànchez, Jose M. Mondelo Gonzalez

Research output: Contribution to journal › Article › Research › peer-review

Abstract

© 2016 Elsevier B.V. We estimate numerically the regularities of a family of Strange Non-Chaotic Attractors related with one of the models studied in (Grebogi et al., 1984) (see also Keller, 1996). To estimate these regularities we use wavelet analysis in the spirit of de la Llave and Petrov (2002) together with some ad-hoc techniques that we develop to overcome the theoretical difficulties that arise in the application of the method to the particular family that we consider. These difficulties are mainly due to the facts that we do not have an explicit formula for the attractor and it is discontinuous almost everywhere for some values of the parameters. Concretely we propose an algorithm based on the Fast Wavelet Transform. Also a quality check of the wavelet coefficients and regularity estimates is done.

Original language	English
Pages (from-to)	74-89
Journal	Physica D: Nonlinear Phenomena
Volume	347
DOIs	https://doi.org/10.1016/j.physd.2016.12.006
Publication status	Published - 15 May 2017

Keywords

Quasiperiodically forced system
Regularity
Wavelets

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title = "A numerical estimate of the regularity of a family of Strange Non-Chaotic Attractors",

abstract = "{\textcopyright} 2016 Elsevier B.V. We estimate numerically the regularities of a family of Strange Non-Chaotic Attractors related with one of the models studied in (Grebogi et al., 1984) (see also Keller, 1996). To estimate these regularities we use wavelet analysis in the spirit of de la Llave and Petrov (2002) together with some ad-hoc techniques that we develop to overcome the theoretical difficulties that arise in the application of the method to the particular family that we consider. These difficulties are mainly due to the facts that we do not have an explicit formula for the attractor and it is discontinuous almost everywhere for some values of the parameters. Concretely we propose an algorithm based on the Fast Wavelet Transform. Also a quality check of the wavelet coefficients and regularity estimates is done.",

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TY - JOUR

T1 - A numerical estimate of the regularity of a family of Strange Non-Chaotic Attractors

AU - Alsedà i Soler, Lluís

AU - Romero i Sànchez, David

AU - Mondelo Gonzalez, Jose M.

PY - 2017/5/15

Y1 - 2017/5/15

N2 - © 2016 Elsevier B.V. We estimate numerically the regularities of a family of Strange Non-Chaotic Attractors related with one of the models studied in (Grebogi et al., 1984) (see also Keller, 1996). To estimate these regularities we use wavelet analysis in the spirit of de la Llave and Petrov (2002) together with some ad-hoc techniques that we develop to overcome the theoretical difficulties that arise in the application of the method to the particular family that we consider. These difficulties are mainly due to the facts that we do not have an explicit formula for the attractor and it is discontinuous almost everywhere for some values of the parameters. Concretely we propose an algorithm based on the Fast Wavelet Transform. Also a quality check of the wavelet coefficients and regularity estimates is done.

AB - © 2016 Elsevier B.V. We estimate numerically the regularities of a family of Strange Non-Chaotic Attractors related with one of the models studied in (Grebogi et al., 1984) (see also Keller, 1996). To estimate these regularities we use wavelet analysis in the spirit of de la Llave and Petrov (2002) together with some ad-hoc techniques that we develop to overcome the theoretical difficulties that arise in the application of the method to the particular family that we consider. These difficulties are mainly due to the facts that we do not have an explicit formula for the attractor and it is discontinuous almost everywhere for some values of the parameters. Concretely we propose an algorithm based on the Fast Wavelet Transform. Also a quality check of the wavelet coefficients and regularity estimates is done.

KW - Quasiperiodically forced system

KW - Regularity

KW - Wavelets

U2 - https://doi.org/10.1016/j.physd.2016.12.006

DO - https://doi.org/10.1016/j.physd.2016.12.006

M3 - Article

SN - 0167-2789

VL - 347

SP - 74

EP - 89

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

ER -

A numerical estimate of the regularity of a family of Strange Non-Chaotic Attractors

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Keywords

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