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

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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

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