We consider a nongeneric family of 3D Filippov linear systems with a discontinuity plane that have two parallel tangency lines, such that the region between them is the sliding region. We are interested in finding under what conditions the family has a crossing limit cycle, when the sliding region changes its stability. We call this phenomenon the pseudo-Hopf bifurcation. This class of systems is motivated by piecewise-linear control systems which have not yet been treated in the context of crossing limit cycles.
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