Confirmation of the Afraimovich-Shilnikov torus-breakdown theorem via a torus circuit

The Afraimovich-Shilnikov theorem on 2D torus breakdown is formulated and used to carry out a detailed numerical investigation of the bifurcation routes from the torus to chaos in a third-order torus circuit. Three scenarios of transition to chaos due to torus breakdown take place in this circuit in complete agreement with the theorem: 1) period-doubling bifurcations of the phase-locked limit cycles; 2) saddle-node bifurcation in the presence of a homoclinic structure; and 3) soft transition due to the loss of torus smoothness.>