Unfolding a Codimension-Two, Discontinuous, Andronov-Hopf Bifurcation
Dynamical Systems
2009-11-13 v1
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 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.
Cite
@article{arxiv.0804.3101,
title = {Unfolding a Codimension-Two, Discontinuous, Andronov-Hopf Bifurcation},
author = {D. J. W. Simpson and J. D. Meiss},
journal= {arXiv preprint arXiv:0804.3101},
year = {2009}
}
Comments
19 pages, 4 figures