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A study of resonance tongues near a Chenciner bifurcation using MatContM

Willy Govaerts UGent, Yuri A Kuznetsov, Hil GE Meijer and Niels Neirynck UGent (2011) Proceedings of the 7th European Nonlinear Dynamics Conference (ENOC 2011).
abstract
MatcontM is a matlab toolbox for numerical analysis of bifurcations of periodic orbits of maps. It computes codim 1 bifurcation curves and supports the computation of normal coefficients including branch switching from codim 2 points to secondary curves. Recently, the initialization and computation of connecting orbits was improved. Moreover, a graphical user interface was added enabling interactive control of all these computations. We demonstrate the use of the toolbox in a study of Arnol’d tongues near a degenerate Neimark-Sacker (Chenciner) bifurcation. Here we illustrate the recent theory of [4] how resonance tongues interact with a quasi-periodic saddle-node bifurcation of invariant curves in maps. Using normal form coefficients we find evidence for one of their cases, but not the other. Actually, we find another unfolding, i.e. a third possibility. We also give numerical evidence for the existence of a quasi-periodic cusp bifurcation of invariant curves.
Please use this url to cite or link to this publication:
author
organization
year
type
conference
publication status
published
subject
keyword
bifurcation, Map, Matcon, resonance
in
Proceedings of the 7th European Nonlinear Dynamics Conference (ENOC 2011)
editor
D Bernardini, G Rega and F Romeo
article_number
MS-03
pages
5 pages
publisher
Sapienza Universita di Roma
place of publication
Rome, Italy
conference name
7th European Nonlinear Dynamics Conference (ENOC 2011)
conference location
Rome, Italy
conference start
2011-07-24
conference end
2011-07-29
ISBN
9788890623424
DOI
10.3267/ENOC2011Rome
language
English
UGent publication?
yes
classification
C1
copyright statement
I have transferred the copyright for this publication to the publisher
id
2129428
handle
http://hdl.handle.net/1854/LU-2129428
alternative location
http://w3.uniroma1.it/dsg/enoc2011/proceedings/pdf/Govaerts_et_al_6page.pdf
date created
2012-06-01 16:00:30
date last changed
2012-06-18 14:45:39
@inproceedings{2129428,
  abstract     = {MatcontM is a matlab toolbox for numerical analysis of bifurcations of periodic orbits of maps. It computes codim 1 bifurcation curves and supports the computation of normal coefficients including branch switching from codim 2 points to secondary curves. Recently, the initialization and computation of connecting orbits was improved. Moreover, a graphical user interface was added enabling interactive control of all these computations. We demonstrate the use of the toolbox in a study of Arnol{\textquoteright}d tongues near a degenerate Neimark-Sacker (Chenciner) bifurcation. Here we illustrate the recent theory of [4] how resonance tongues interact with a quasi-periodic saddle-node bifurcation of invariant curves in maps. Using normal form coefficients we find evidence for one of their cases, but not the other. Actually, we find another unfolding, i.e. a third possibility. We also give numerical evidence for the existence of a quasi-periodic cusp bifurcation of invariant curves.},
  articleno    = {MS-03},
  author       = {Govaerts, Willy and Kuznetsov, Yuri A and Meijer, Hil GE and Neirynck, Niels},
  booktitle    = {Proceedings of the 7th European Nonlinear Dynamics Conference (ENOC 2011)},
  editor       = {Bernardini, D and Rega, G and Romeo, F},
  isbn         = {9788890623424},
  keyword      = {bifurcation,Map,Matcon,resonance},
  language     = {eng},
  location     = {Rome, Italy},
  pages        = {5},
  publisher    = {Sapienza Universita di Roma},
  title        = {A study of resonance tongues near a Chenciner bifurcation using MatContM},
  url          = {http://dx.doi.org/10.3267/ENOC2011Rome},
  year         = {2011},
}

Chicago
Govaerts, Willy, Yuri A Kuznetsov, Hil GE Meijer, and Niels Neirynck. 2011. “A Study of Resonance Tongues Near a Chenciner Bifurcation Using MatContM.” In Proceedings of the 7th European Nonlinear Dynamics Conference (ENOC 2011), ed. D Bernardini, G Rega, and F Romeo. Rome, Italy: Sapienza Universita di Roma.
APA
Govaerts, W., Kuznetsov, Y. A., Meijer, H. G., & Neirynck, N. (2011). A study of resonance tongues near a Chenciner bifurcation using MatContM. In D. Bernardini, G. Rega, & F. Romeo (Eds.), Proceedings of the 7th European Nonlinear Dynamics Conference (ENOC 2011). Presented at the 7th European Nonlinear Dynamics Conference (ENOC 2011), Rome, Italy: Sapienza Universita di Roma.
Vancouver
1.
Govaerts W, Kuznetsov YA, Meijer HG, Neirynck N. A study of resonance tongues near a Chenciner bifurcation using MatContM. In: Bernardini D, Rega G, Romeo F, editors. Proceedings of the 7th European Nonlinear Dynamics Conference (ENOC 2011). Rome, Italy: Sapienza Universita di Roma; 2011.
MLA
Govaerts, Willy, Yuri A Kuznetsov, Hil GE Meijer, et al. “A Study of Resonance Tongues Near a Chenciner Bifurcation Using MatContM.” Proceedings of the 7th European Nonlinear Dynamics Conference (ENOC 2011). Ed. D Bernardini, G Rega, & F Romeo. Rome, Italy: Sapienza Universita di Roma, 2011. Print.