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