Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA.
Neural Comput. 2012 Dec;24(12):3111-25. doi: 10.1162/NECO_a_00370. Epub 2012 Sep 12.
We introduce a simple two-dimensional model that extends the Poincaré oscillator so that the attracting limit cycle undergoes a saddle node bifurcation on an invariant circle (SNIC) for certain parameter values. Arbitrarily close to this bifurcation, the phase-resetting curve (PRC) continuously depends on parameters, where its shape can be not only primarily positive or primarily negative but also nearly sinusoidal. This example system shows that one must be careful inferring anything about the bifurcation structure of the oscillator from the shape of its PRC.
我们引入了一个简单的二维模型，该模型扩展了 Poincaré 振荡器，使得在某些参数值下，吸引的极限环在不变圆上经历鞍结分岔 (SNIC)。在这个分岔点附近，相位重置曲线 (PRC) 连续地依赖于参数，其形状不仅可以主要是正的或主要是负的，而且还可以几乎是正弦的。这个示例系统表明，人们必须小心从振荡器的 PRC 形状推断任何关于其分岔结构的信息。
