title: Unfolding a codimension-two, discontinuous, Andronov-Hopf bifurcation.
abstract: 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 that 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.
authors.affiliation: Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309-0526, USA.
authors.forename: D J W
authors.initials: DJ
authors.lastname: Simpson
authors.forename: J D
authors.initials: JD
authors.lastname: Meiss
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D009991:Oscillometry / Q000379:methods*