<abstract xmlns="http://www.w3.org/1999/xhtml"><p>This paper is devoted to the analysis of bidimensional piecewise linear systems with hysteresis coming from a reduction of symmetric 3D systems with slow-fast dynamics. We concentrate our attention on the saddle dynamics cases, determining the existence of periodic orbits as well as their stability, and possible bifurcations. Dealing with reachable saddles not in the central hysteresis band, we show the existence of subcritical/supercritical heteroclinic bifurcations as well as saddle-node bifurcations of periodic orbits.</p></abstract>

This paper is devoted to the analysis of bidimensional piecewise linear systems with hysteresis coming from a reduction of symmetric 3D systems with slow-fast dynamics. We concentrate our attention on the saddle dynamics cases, determining the existence of periodic orbits as well as their stability, and possible bifurcations. Dealing with reachable saddles not in the central hysteresis band, we show the existence of subcritical/supercritical heteroclinic bifurcations as well as saddle-node bifurcations of periodic orbits.

Bifurcation Analysis of Hysteretic Systems with Saddle Dynamics

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Bifurcation Analysis of Hysteretic Systems with Saddle Dynamics"}

This paper is devoted to the analysis of bidimensional piecewise linear systems with hysteresis coming from a reduction of symmetric 3D systems with slow-fast...

Bifurcation Analysis of Hysteretic Systems with Saddle Dynamics

Publié en ligne: 04 nov. 2017

Pages: 449 - 464

Reçu: 06 avr. 2017

Accepté: 04 nov. 2017

DOI: https://doi.org/10.21042/AMNS.2017.2.00036

Mots clés
Bifurcations, Hysteresis, Periodic Orbits

© 2017 Marina Esteban, Enrique Ponce, Francisco Torres, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Bifurcation Analysis of Hysteretic Systems with Saddle Dynamics

Publié en ligne: 04 nov. 2017

Pages: 449 - 464

Reçu: 06 avr. 2017

Accepté: 04 nov. 2017

DOI: https://doi.org/10.21042/AMNS.2017.2.00036

Mots clésBifurcations, Hysteresis, Periodic Orbits

© 2017 Marina Esteban, Enrique Ponce, Francisco Torres, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Mots clés
Bifurcations, Hysteresis, Periodic Orbits