Simpson D J W, Meiss J D
Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309-0526, USA.
Chaos. 2008 Sep;18(3):033125. doi: 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 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.
我们展示了平面上一个分段光滑的自治常微分方程连续系统中同时出现不连续分岔和安德罗诺夫 - 霍普夫分岔的余维二情形的一种展开。我们发现霍普夫环经历了一个擦边分岔，之后可能很快接着轨道的鞍结分岔。我们推导了从余维二分岔发出的分岔曲线的标度律。
