Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 332, Issue -, Pages 219-277Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2022.05.028
Keywords
Regularization of Filippov systems; Grazing-sliding bifurcation; Saddle-node bifurcation; Hysteresis; Chaotic behavior
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Funding
- ERDF A way of making Europe [PGC2018-098676-B-100, MCIN/AEI/10.13039/501100011033]
- Catalan Institution for Research and Advanced Studies via an ICREA Academia Prize 2019
- Spanish State Research Agency, through the Severo Ochoa and Maria de Maeztu Program for Centers and Units of Excellence in RD [CEX2020-001084-M]
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In this paper, we present two ways of regularizing a one parameter family of piece-wise smooth dynamical systems undergoing a codimension one grazing-sliding global bifurcation of periodic orbits. Our results show that when a tangency appears, the hysteretic regularization will generate chaotic dynamics.
We present two ways of regularizing a one parameter family of piece-wise smooth dynamical systems undergoing a codimension one grazing-sliding global bifurcation of periodic orbits. First we use the Sotomayor-Teixeira regularization and prove that the regularized family has a saddle-node bifurcation of periodic orbits. Then we perform a hysteretic regularization and show that the regularized family has chaotic dynamics. Our result shows that, in spite that the two regularizations will give the same dynamics in the sliding modes, when a tangency appears the hysteretic process generates chaotic dynamics. (c) 2022 Elsevier Inc. All rights reserved.
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