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
1DESP, University of Urbino, Urbino, Italy
2Institute of Parallel and Distributed Systems, University of Stuttgart, Germany
3National 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 
@article{EP_2012_36_a9,
     author = {Laura Gardini and Viktor Avrutin and Michael Schanz and Albert Granados and Iryna Sushko},
     title = {Organizing centers in parameter space of discontinuous {1D} maps. {The} case of increasing/decreasing branches},
     journal = {ESAIM. Proceedings},
     pages = {106--120},
     year = {2012},
     volume = {36},
     doi = {10.1051/proc/201236009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201236009/}
}
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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

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