Birth of bilayered torus and torus breakdown in a piecewise-smooth dynamical system |
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Institution: | 1. Kursk State Technical University, Department of Computer Science, 50 Years of October Str., 94, Kursk 305040, Russia;2. Complex Systems Group, Department of Physics, The Technical University of Denmark, 2800 Lyngby, Denmark |
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Abstract: | Border-collision bifurcations arise when the periodic trajectory of a piecewise-smooth system under variation of a parameter crosses into a region with different dynamics. Considering a three-dimensional map describing the behavior of a DC/DC power converter, the Letter discusses a new type of border-collision bifurcation that leads to the birth of a “bilayered torus”. This torus consists of the union of two saddle cycles, their unstable manifolds, and a stable focus cycle. When changing the parameters, the bilayered torus transforms through a border-collision bifurcation into a resonance torus containing the stable cycle and a saddle. The Letter also presents scenarios for torus destruction through homoclinic and heteroclinic tangencies. |
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