Abstract
In this work a homoclinic-like loop of a 3D piecewise smooth vector field passing through a typical singularity is analyzed. We have shown that such a loop is robust in one-parameter families of Filippov systems. The basin of attraction of this connection is computed as well as its bifurcation diagram. It is worthwhile to mention that this phenomenon has no counterpart in the smooth world. Our approach relies on the analysis of first return maps and the technique used in this scenario is much more complex than the usual analysis of Poincaré maps in planar Filippov systems.
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