Six limit cycles in the Bonhöffer-van der Pol piecewise linear oscillator via saddle-node bifurcations.

Extending a previous analysis of the Hopf bifurcation at infinity in symmetric piecewise linear differential systems with three zones, which is responsible for the appearance of a large amplitude limit cycle, in this work we analyze the degeneration of such a bifurcation at infinity, providing a theoretical result that guarantees the existence of a saddle-node bifurcation curve of periodic orbits. Combining this new result with other known bifurcation results, we analyze an extended Bonhöffer-van der Pol piecewise linear electronic oscillator. We get a deeper insight on the dynamical richness of this oscillator, showing rigorously the simultaneous existence of six limit cycles in some region of its bifurcation set.}