论文标题
杂斜网络附近的有限切换
Finite switching near heteroclinic networks
论文作者
论文摘要
我们解决了在强大的杂斜网络附近的动力学中可以观察到的复杂性水平。我们表明，无限切换是通往混乱的路径，并不存在于杂斜网络附近，因此每个节点处的Jacobian矩阵的特征值都是真实的。此外，对于从属于一个以上杂斜周期的节点开始的路径，我们找到了可以在任何此类路径中存在的这种节点的数量的绑定。这种狭窄的动力学与杂斜网络文献中的示例形成鲜明对比，使一个节点处的雅各布矩阵的特征值很复杂。
We address the level of complexity that can be observed in the dynamics near a robust heteroclinic network. We show that infinite switching, which is a path towards chaos, does not exist near a heteroclinic network such that the eigenvalues of the Jacobian matrix at each node are all real. Furthermore, for a path starting at a node that belongs to more than one heteroclinic cycle, we find a bound for the number of such nodes that can exist in any such path. This constricted dynamics is in stark contrast with examples in the literature of heteroclinic networks such that the eigenvalues of the Jacobian matrix at one node are complex.
