Bifurcation of periodic and chaotic solutions in discontinuous systems

Michal Fečkan

Archivum Mathematicum (1998)

  • Volume: 034, Issue: 1, page 73-82
  • ISSN: 0044-8753

Abstract

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Chaos generated by the existence of Smale horseshoe is the well-known phenomenon in the theory of dynamical systems. The Poincaré-Andronov-Melnikov periodic and subharmonic bifurcations are also classical results in this theory. The purpose of this note is to extend those results to ordinary differential equations with multivalued perturbations. We present several examples based on our recent achievements in this direction. Singularly perturbed problems are studied as well. Applications are given to ordinary differential equations with both dry friction and relay hysteresis terms.

How to cite

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Fečkan, Michal. "Bifurcation of periodic and chaotic solutions in discontinuous systems." Archivum Mathematicum 034.1 (1998): 73-82. <http://eudml.org/doc/248196>.

@article{Fečkan1998,
abstract = {Chaos generated by the existence of Smale horseshoe is the well-known phenomenon in the theory of dynamical systems. The Poincaré-Andronov-Melnikov periodic and subharmonic bifurcations are also classical results in this theory. The purpose of this note is to extend those results to ordinary differential equations with multivalued perturbations. We present several examples based on our recent achievements in this direction. Singularly perturbed problems are studied as well. Applications are given to ordinary differential equations with both dry friction and relay hysteresis terms.},
author = {Fečkan, Michal},
journal = {Archivum Mathematicum},
keywords = {Chaotic and periodic solutions; differential inclusions; relay hysteresis; chaotic and periodic solutions; differential inclusions; relay hysteresis},
language = {eng},
number = {1},
pages = {73-82},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Bifurcation of periodic and chaotic solutions in discontinuous systems},
url = {http://eudml.org/doc/248196},
volume = {034},
year = {1998},
}

TY - JOUR
AU - Fečkan, Michal
TI - Bifurcation of periodic and chaotic solutions in discontinuous systems
JO - Archivum Mathematicum
PY - 1998
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 034
IS - 1
SP - 73
EP - 82
AB - Chaos generated by the existence of Smale horseshoe is the well-known phenomenon in the theory of dynamical systems. The Poincaré-Andronov-Melnikov periodic and subharmonic bifurcations are also classical results in this theory. The purpose of this note is to extend those results to ordinary differential equations with multivalued perturbations. We present several examples based on our recent achievements in this direction. Singularly perturbed problems are studied as well. Applications are given to ordinary differential equations with both dry friction and relay hysteresis terms.
LA - eng
KW - Chaotic and periodic solutions; differential inclusions; relay hysteresis; chaotic and periodic solutions; differential inclusions; relay hysteresis
UR - http://eudml.org/doc/248196
ER -

References

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