Geodesic
Organizing centers in parameter space of discontinuous 1D maps. The case of increasing/decreasing branches
Laura Gardini1 ; Viktor Avrutin2 ; Michael Schanz2 ; Albert Granados2 ; Iryna Sushko3
1 DESP, University of Urbino, Urbino, Italy
2 Institute of Parallel and Distributed Systems, University of Stuttgart, Germany
3 National Academy of Sciences of Ukraine, and Kiev School of Economics, Kiev, Ukraine
ESAIM. Proceedings, Tome 36 (2012), pp. 106-120.

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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.
DOI : 10.1051/proc/201236009

Laura Gardini 1 ; Viktor Avrutin 2 ; Michael Schanz 2 ; Albert Granados 2 ; Iryna Sushko 3

1 DESP, University of Urbino, Urbino, Italy
2 Institute of Parallel and Distributed Systems, University of Stuttgart, Germany
3 National Academy of Sciences of Ukraine, and Kiev School of Economics, Kiev, Ukraine 
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     title = {Organizing centers in parameter space of discontinuous {1D} maps. {The} case of increasing/decreasing branches},
     journal = {ESAIM. Proceedings},
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Laura Gardini; Viktor Avrutin; Michael Schanz; Albert Granados; Iryna Sushko. Organizing centers in parameter space of discontinuous 1D maps. The case of increasing/decreasing branches. ESAIM. Proceedings, Tome 36 (2012), pp. 106-120. doi : 10.1051/proc/201236009. http://geodesic.mathdoc.fr/articles/10.1051/proc/201236009/

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