Article
Bifurcation Analysis of Hysteretic Systems with Saddle Dynamics
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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
M. Esteban, E. Ponce and F. Torres, “Bifurcation analysis of hysteretic systems with saddle dynamics,” Applied Mathematics and Nonlinear Sciences, vol. 2, no. 2, pp. 449–464, 2017, doi: 10.21042/AMNS.2017.2.00036.
Esteban M, Ponce E, Torres F. Bifurcation analysis of hysteretic systems with saddle dynamics. Applied Mathematics and Nonlinear Sciences. 2017;2(2):449–464. doi:10.21042/AMNS.2017.2.00036.
Esteban, M., Ponce, E. and Torres, F. (2017), ‘Bifurcation analysis of hysteretic systems with saddle dynamics’, Applied Mathematics and Nonlinear Sciences, 2(2), pp. 449–464. Available at: https://doi.org/10.21042/AMNS.2017.2.00036.
Esteban, Marina, et al. “Bifurcation Analysis of Hysteretic Systems with Saddle Dynamics.” Applied Mathematics and Nonlinear Sciences, vol. 2, no. 2, 2017, pp. 449–464. https://doi.org/10.21042/AMNS.2017.2.00036.
Esteban, Marina, Enrique Ponce, and Francisco Torres. “Bifurcation Analysis of Hysteretic Systems with Saddle Dynamics.” Applied Mathematics and Nonlinear Sciences 2, no. 2 (2017): 449–464. https://doi.org/10.21042/AMNS.2017.2.00036.
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Published by: Engineering Journals


