<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

Published Online: Nov 04, 2017

Page range: 449 - 464

Received: Apr 06, 2017

Accepted: Nov 04, 2017

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

Keywords
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

Published Online: Nov 04, 2017

Page range: 449 - 464

Received: Apr 06, 2017

Accepted: Nov 04, 2017

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

KeywordsBifurcations, 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.

Keywords
Bifurcations, Hysteresis, Periodic Orbits