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The topological reconstruction of forced oscillators

Solari, Hernan G. and Natiello, Mario LU (2009) In Chaos, Solitons & Fractals 42(4). p.2023-2034
Abstract
Periodically forced oscillators are among the simplest dynamical systems capable to display chaos. They can be described by the variables position and velocity, together with the phase of the force. Their phase-space corresponds therefore to R-2 x S-1. The organization of the periodic orbits can be displayed with braids having only positive crossings. Topological characterization of dynamical systems actually began to be explored in physics on this family of problems. In this work we show that, in general, it is not possible to produce a 3-dimensional imbedding of the solutions of a forced oscillator in terms of differential imbeddings based on sampling the position only. However, it may be possible to uncover a description of the phase... (More)
Periodically forced oscillators are among the simplest dynamical systems capable to display chaos. They can be described by the variables position and velocity, together with the phase of the force. Their phase-space corresponds therefore to R-2 x S-1. The organization of the periodic orbits can be displayed with braids having only positive crossings. Topological characterization of dynamical systems actually began to be explored in physics on this family of problems. In this work we show that, in general, it is not possible to produce a 3-dimensional imbedding of the solutions of a forced oscillator in terms of differential imbeddings based on sampling the position only. However, it may be possible to uncover a description of the phase variable from the sampled time-series, thus producing a faithful representation of the data. We proceed to formulate new tests in order to check whether proposed imbeddings can be accepted as such. We illustrate the manuscript throughout with an example corresponding to a model of Benard-Marangoni convection. (C) 2009 Elsevier Ltd. All rights reserved. (Less)
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organization
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type
Contribution to journal
publication status
published
subject
in
Chaos, Solitons & Fractals
volume
42
issue
4
pages
2023 - 2034
publisher
Elsevier
external identifiers
  • wos:000269190000010
  • scopus:67650995792
ISSN
0960-0779
DOI
10.1016/j.chaos.2009.03.167
language
English
LU publication?
yes
id
3a5271c4-bacf-49a9-a198-64f17bcb6f09 (old id 1477072)
date added to LUP
2009-09-23 15:10:17
date last changed
2017-03-14 13:42:24
@article{3a5271c4-bacf-49a9-a198-64f17bcb6f09,
  abstract     = {Periodically forced oscillators are among the simplest dynamical systems capable to display chaos. They can be described by the variables position and velocity, together with the phase of the force. Their phase-space corresponds therefore to R-2 x S-1. The organization of the periodic orbits can be displayed with braids having only positive crossings. Topological characterization of dynamical systems actually began to be explored in physics on this family of problems. In this work we show that, in general, it is not possible to produce a 3-dimensional imbedding of the solutions of a forced oscillator in terms of differential imbeddings based on sampling the position only. However, it may be possible to uncover a description of the phase variable from the sampled time-series, thus producing a faithful representation of the data. We proceed to formulate new tests in order to check whether proposed imbeddings can be accepted as such. We illustrate the manuscript throughout with an example corresponding to a model of Benard-Marangoni convection. (C) 2009 Elsevier Ltd. All rights reserved.},
  author       = {Solari, Hernan G. and Natiello, Mario},
  issn         = {0960-0779},
  language     = {eng},
  number       = {4},
  pages        = {2023--2034},
  publisher    = {Elsevier},
  series       = {Chaos, Solitons & Fractals},
  title        = {The topological reconstruction of forced oscillators},
  url          = {http://dx.doi.org/10.1016/j.chaos.2009.03.167},
  volume       = {42},
  year         = {2009},
}