On 3-Parameter Families of Piecewise Smooth Vector Fields in the Plane
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This paper is concerned with the local bifurcation analysis around typical singularities of piecewise smooth planar dynamical systems. Three-parameter families of a class of nonsmooth vector fields are studied, and the bifurcation diagrams are exhibited. Our main results describe a particular unfolding of the so-called fold-cusp singularity by means of the variation of 3 parameters.