2022
DOI: 10.48550/arxiv.2202.05027
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Blowup analysis of a hysteresis model based upon singular perturbations

Abstract: In this paper, we provide a geometric analysis of a new hysteresis model that is based upon singular perturbations. Here hysteresis refers to a type of regularization of piecewise smooth differential equations where the past of a trajectory, in a small neighborhood of the discontinuity set, determines the vector-field at present. In fact, in the limit where the neighborhood of the discontinuity becomes smaller, hysteresis converges in an appropriate sense to Filippov's sliding vector-field. Recently, however,i… Show more

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Cited by 1 publication
(3 citation statements)
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“…using (40) and (41). The number of equilibria of the reduced problem on S 2 are therefore given by the roots of the rational function…”
Section: Viral Blipmentioning
confidence: 99%
See 2 more Smart Citations
“…using (40) and (41). The number of equilibria of the reduced problem on S 2 are therefore given by the roots of the rational function…”
Section: Viral Blipmentioning
confidence: 99%
“…11(a). These connections are organized around the point (x c , 0), recall (41). In fact, for each x 1 > x c , we can write the connections from (x 1 , 0) to (x 0 , 0) as graphs over…”
Section: Viral Blipmentioning
confidence: 99%
See 1 more Smart Citation