The pseudo-Hopf bifurcation and derived attractors in 3D Filippov linear systems with a Teixeira singularity

Consider the generic family of 3D Filippov linear systems that possess a double-tangency singularity of Teixeira type. We are interested in finding mechanisms for the emergence of an attractor from such a singularity, like a crossing limit cycle, an invariant torus, or a strange attractor. For this, we unfold the pseudo-Hopf bifurcation for this class of systems in order to guarantee the existence of a crossing limit cycle and, subsequently, from this attractor, obtain a more intricate one. Two illustrative examples are given in order to show evidence of attractors obtained by means of the proposed strategy. Both theoretical and numerical results are provided for verification and demonstration.