Classification of Filippov Type 3 Singular Points in Planar Bimodal Piecewise Smooth Systems

.We classify Filippov's type 3 singular points of planar bimodal piecewise smooth systems. These singular points consist of fold or cusp tangencies of the vector fields to both sides of a switching surface. For isolated analytic type 3 singular points there are 25 topological classes, up to time reversal. For isolated general type 3 singular points there are 40 topological classes, up to time reversal.Keywordssingularitiespiecewise smooth systemsclassificationMSC codes37C10