Applied Mathematics and Nonlinear Sciences
Journal license

Journal

Applied Mathematics and Nonlinear Sciences


Volume
& Issue

Volume 2, Issue 2


Published
on

November 4, 2017


Pages

449-464


DOI

Article

Bifurcation Analysis of Hysteretic Systems with Saddle Dynamics

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Authors

Marina Esteban Affiliation:
Departamento de Matemática Aplicada II, Universidad de Sevilla. Escuela Técnica Superior de Ingeniería, Camino de los Descubrimientos s/n 41092, Sevilla, Spain
, Enrique Ponce Affiliation:
Departamento de Matemática Aplicada II, Universidad de Sevilla. Escuela Técnica Superior de Ingeniería, Camino de los Descubrimientos s/n 41092, Sevilla, Spain
and Francisco Torres Affiliation:
Departamento de Matemática Aplicada II, Universidad de Sevilla. Escuela Técnica Superior de Ingeniería, Camino de los Descubrimientos s/n 41092, Sevilla, Spain


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.


Keywords

Bifurcations, Hysteresis, Periodic Orbits, 34C23, 34C55, 34C05


Citation

Esteban, M., Ponce, E., & Torres, F. (2017). Bifurcation analysis of hysteretic systems with saddle dynamics. Applied Mathematics and Nonlinear Sciences, 2(2), 449–464. https://doi.org/10.21042/AMNS.2017.2.00036

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