Unfolding a Codimension-Two, Discontinuous, Andronov-Hopf Bifurcation

Details Unfolding a Codimension-Two, Discontinuous, Andronov-Hopf Bifurcation Unfolding a Codimension-Two, Discontinuous, Andronov-Hopf Bifurcation

2008-04-18

arxiv.org/abs/0804.3101v1

Mathematics

Dynamical Systems

19 pages, 4 figures

Scientific paper

10.1063/1.2976165

We present an unfolding of the codimension-two scenario of the simultaneous occurrence of a discontinuous bifurcation and an Andronov-Hopf bifurcation in a piecewise-smooth, continuous system of autonomous ordinary differential equations in the plane. We find the Hopf cycle undergoes a grazing bifurcation that may be very shortly followed by a saddle-node bifurcation of the orbit. We derive scaling laws for the bifurcation curves that emanate from the codimension-two bifurcation.

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