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讨论多余维Hopf分叉三阶规范形的普适开折形成的网络更进一步的复杂动力学行为.通过对余维二Hopf分叉的规范形网络多级分叉的分析,发现在参数空间的某个区域会出现二环面,将S形非线性加入规范形网络,在出现二环面的区域内可以出现混沌.本文给出了该混沌吸引子的相图及其二阶Poincare映射的图景.由这些图可以看到该混沌吸引子具有非常奇妙的形态:某些二阶Poincare映射像一只逼真的蝴蝶.
We discuss the complex dynamics behavior of the network formed by universal folding of the extra-dimensional Hopf bifurcated third-order normal form. Based on the analysis of canonical Hopf bifurcations in canonical form network, it is found that in a certain region of parameter space, a bicyclic surface appears and the S-shape nonlinearity is added to the canonical form network. There can be chaos inside. In this paper, the phase diagram of this chaotic attractor and its second-order Poincare mapping are given. It can be seen from these figures that the chaotic attractor has a very fantastic morphology: Some second-order Poincare maps behave like a realistic butterfly.