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

Gardini, Laura, et al. Fournier-Prunaret, D., Gardini, L., and Reich, L., eds. " Organizing centers in parameter space of discontinuous 1D maps. The case of increasing/decreasing branches ." ESAIM: Proceedings 36 (2012): 106-120. <http://eudml.org/doc/251250>.

@article{Gardini2012,
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.},
author = {Gardini, Laura, Avrutin, Viktor, Schanz, Michael, Granados, Albert, Sushko, Iryna},
editor = {Fournier-Prunaret, D., Gardini, L., Reich, L.},
journal = {ESAIM: Proceedings},
keywords = {piecewise smooth maps; border collision bifurcations; organizing centers},
language = {eng},
month = {8},
pages = {106-120},
publisher = {EDP Sciences},
title = { Organizing centers in parameter space of discontinuous 1D maps. The case of increasing/decreasing branches },
url = {http://eudml.org/doc/251250},
volume = {36},
year = {2012},
}

TY - JOUR
AU - Gardini, Laura
AU - Avrutin, Viktor
AU - Schanz, Michael
AU - Granados, Albert
AU - Sushko, Iryna
AU - Fournier-Prunaret, D.
AU - Gardini, L.
AU - Reich, L.
TI - Organizing centers in parameter space of discontinuous 1D maps. The case of increasing/decreasing branches
JO - ESAIM: Proceedings
DA - 2012/8//
PB - EDP Sciences
VL - 36
SP - 106
EP - 120
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.
LA - eng
KW - piecewise smooth maps; border collision bifurcations; organizing centers
UR - http://eudml.org/doc/251250
ER -