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• W2040606494 abstract "In this paper we use the blowup method of Dumortier and Roussarie, in the formulation due to Krupa and Szmolyan, to study the regularization of singularities of piecewise smooth dynamical systems in $mathbb R^3$. Using the regularization method of Sotomayor and Teixeira, we first demonstrate the power of our approach by considering the case of a fold line. We quickly extend a main result of Reves and Seara in a simple manner. Then, for the two-fold singularity, we show that the regularized system only fully retains the features of the singular canards in the piecewise smooth system in the cases when the sliding region does not include a full sector of singular canards. In particular, we show that every locally unique primary singular canard persists the regularizing perturbation. For the case of a sector of primary singular canards, we show that the regularized system contains a canard, provided a certain nonresonance condition holds. Finally, we provide numerical evidence for the existence of secondary canards near resonance." @default.
• W2040606494 created "2016-06-24" @default.
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• W2040606494 date "2015-01-01" @default.
• W2040606494 modified "2023-09-25" @default.
• W2040606494 title "On the Use of Blowup to Study Regularizations of Singularities of Piecewise Smooth Dynamical Systems in $mathbb{R}^3$" @default.
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• W2040606494 doi "https://doi.org/10.1137/140980995" @default.
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