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• W1998767953 abstract "A two-fold singularity is a point on a discontinuity surface of a piecewise-smooth vector field at which the vector field is tangent to the surface on both sides. Due to the double tangency, forward evolution from a two-fold is typically ambiguous. This is an especially serious issue for two-folds that are reached by the forward orbits of a non-zero measure set of initial points. The purpose of this paper is to explore the concept of perturbing the vector field so that forward evolution is well-defined, and characterising the perturbed dynamics in the limit that the size of the perturbation tends to zero. This concept is applied to a two-fold in two dimensions. Three forms of perturbation: hysteresis, time-delay, and noise, are analysed individually. In each case, the limit leads to a novel probabilistic notion of forward evolution from the two-fold." @default.
• W1998767953 created "2016-06-24" @default.
• W1998767953 creator A5067953112 @default.
• W1998767953 date "2013-04-16" @default.
• W1998767953 modified "2023-09-27" @default.
• W1998767953 title "On resolving singularities of piecewise-smooth discontinuous vector fields via small perturbations" @default.
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• W1998767953 hasPublicationYear "2013" @default.
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