Organizing centers in parameter space of discontinuous 1D maps. The case of increasing/decreasing branches

Laura Gardini, Viktor Avrutin, Michael Michael Schanz, Albert Granados, Iryna Sushko

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

37 Downloads (Pure)

Abstract

This work contributes to classify the dynamic behaviors of piecewise smooth systems in which border collision bifurcations characterize the qualitative changes in the dynamics. A central point of our investigation is the intersection of two border collision bifurcation curves in a parameter plane. This problem is also associated with the continuity breaking in a fixed point of a piecewise smooth map. We will relax the hypothesis needed in [4] where it was proved that in the case of an increasing/decreasing contracting functions on the left/right side of a border point, at such a crossing point, we have a big-bang bifurcation, from which infinitely many border collision bifurcation curves are issuing.
Original languageEnglish
Title of host publicationESAIM: Proceedings
PublisherEDP Sciences
Publication date2012
Pages106-120
DOIs
Publication statusPublished - 2012
Externally publishedYes
EventEuropean Conference on Iteration Theory (ECIT 2010) - Nants, France
Duration: 12 Sep 201017 Sep 2010

Conference

ConferenceEuropean Conference on Iteration Theory (ECIT 2010)
CountryFrance
CityNants
Period12/09/201017/09/2010
SeriesESAIM: Proceedings and Surveys
NumberApril
Volume36

Keywords

  • Piecewise smooth maps
  • Border collision bifurcations
  • Organizing centers

Cite this

Gardini, L., Avrutin, V., Michael Schanz, M., Granados, A., & Sushko, I. (2012). Organizing centers in parameter space of discontinuous 1D maps. The case of increasing/decreasing branches. In ESAIM: Proceedings (pp. 106-120). EDP Sciences. ESAIM: Proceedings and Surveys, No. April, Vol.. 36 https://doi.org/10.1051/proc/201236009
Gardini, Laura ; Avrutin, Viktor ; Michael Schanz, Michael ; Granados, Albert ; Sushko, Iryna . / Organizing centers in parameter space of discontinuous 1D maps. The case of increasing/decreasing branches. ESAIM: Proceedings. EDP Sciences, 2012. pp. 106-120 (ESAIM: Proceedings and Surveys; No. April, Vol. 36).
@inproceedings{3e4e425c56fb4d9da59fc22d827601a9,
title = "Organizing centers in parameter space of discontinuous 1D maps. The case of increasing/decreasing branches",
abstract = "This work contributes to classify the dynamic behaviors of piecewise smooth systems in which border collision bifurcations characterize the qualitative changes in the dynamics. A central point of our investigation is the intersection of two border collision bifurcation curves in a parameter plane. This problem is also associated with the continuity breaking in a fixed point of a piecewise smooth map. We will relax the hypothesis needed in [4] where it was proved that in the case of an increasing/decreasing contracting functions on the left/right side of a border point, at such a crossing point, we have a big-bang bifurcation, from which infinitely many border collision bifurcation curves are issuing.",
keywords = "Piecewise smooth maps, Border collision bifurcations, Organizing centers",
author = "Laura Gardini and Viktor Avrutin and {Michael Schanz}, Michael and Albert Granados and Iryna Sushko",
year = "2012",
doi = "http://dx.doi.org/10.1051/proc/201236009",
language = "English",
pages = "106--120",
booktitle = "ESAIM: Proceedings",
publisher = "EDP Sciences",
address = "France",

}

Gardini, L, Avrutin, V, Michael Schanz, M, Granados, A & Sushko, I 2012, Organizing centers in parameter space of discontinuous 1D maps. The case of increasing/decreasing branches. in ESAIM: Proceedings. EDP Sciences, ESAIM: Proceedings and Surveys, no. April, vol. 36, pp. 106-120, European Conference on Iteration Theory (ECIT 2010), Nants, France, 12/09/2010. https://doi.org/10.1051/proc/201236009

Organizing centers in parameter space of discontinuous 1D maps. The case of increasing/decreasing branches. / Gardini, Laura; Avrutin, Viktor ; Michael Schanz, Michael; Granados, Albert; Sushko, Iryna .

ESAIM: Proceedings. EDP Sciences, 2012. p. 106-120 (ESAIM: Proceedings and Surveys; No. April, Vol. 36).

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

TY - GEN

T1 - Organizing centers in parameter space of discontinuous 1D maps. The case of increasing/decreasing branches

AU - Gardini, Laura

AU - Avrutin, Viktor

AU - Michael Schanz, Michael

AU - Granados, Albert

AU - Sushko, Iryna

PY - 2012

Y1 - 2012

N2 - This work contributes to classify the dynamic behaviors of piecewise smooth systems in which border collision bifurcations characterize the qualitative changes in the dynamics. A central point of our investigation is the intersection of two border collision bifurcation curves in a parameter plane. This problem is also associated with the continuity breaking in a fixed point of a piecewise smooth map. We will relax the hypothesis needed in [4] where it was proved that in the case of an increasing/decreasing contracting functions on the left/right side of a border point, at such a crossing point, we have a big-bang bifurcation, from which infinitely many border collision bifurcation curves are issuing.

AB - This work contributes to classify the dynamic behaviors of piecewise smooth systems in which border collision bifurcations characterize the qualitative changes in the dynamics. A central point of our investigation is the intersection of two border collision bifurcation curves in a parameter plane. This problem is also associated with the continuity breaking in a fixed point of a piecewise smooth map. We will relax the hypothesis needed in [4] where it was proved that in the case of an increasing/decreasing contracting functions on the left/right side of a border point, at such a crossing point, we have a big-bang bifurcation, from which infinitely many border collision bifurcation curves are issuing.

KW - Piecewise smooth maps

KW - Border collision bifurcations

KW - Organizing centers

U2 - http://dx.doi.org/10.1051/proc/201236009

DO - http://dx.doi.org/10.1051/proc/201236009

M3 - Article in proceedings

SP - 106

EP - 120

BT - ESAIM: Proceedings

PB - EDP Sciences

ER -

Gardini L, Avrutin V, Michael Schanz M, Granados A, Sushko I. Organizing centers in parameter space of discontinuous 1D maps. The case of increasing/decreasing branches. In ESAIM: Proceedings. EDP Sciences. 2012. p. 106-120. (ESAIM: Proceedings and Surveys; No. April, Vol. 36). https://doi.org/10.1051/proc/201236009