Analysis reveals 32 topologically distinct canonical forms in vector fields, suggesting new insights on cusp-fold singularities.
In this paper we obtain 32 canonical forms for 3D piecewise smooth vector fields presenting the so called cusp-fold singularity. All these canonical forms are topologically distinct and collect the main topological aspects of the singularities described. Also, one-parameter bifurcations of these canonical forms are presented and the topologically equivalent piecewise smooth vector fields are obtained.
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