固定低维状态空间中的任意大型异斜网络

S. Castro, Alexander Lohse
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引用次数: 0

摘要

我们考虑n∈n个节点之间的异斜网络,其中唯一的连接是连接每个节点与其相邻节点的连接。我们使用一种构造方法,将所有节点放置在单个一维空间中,并且连接位于坐标平面中,我们证明了使用多项式向量场在R6中对任意数量的节点n健壮地实现这些网络是可能的。这种空间维度的界限(当网络中的节点数量趋于∞时)是一种新颖的现象,并且就所需的空间维度数量而言,对于给定的连接结构,这是朝着更有效的实现方法迈出的一步。我们简要地讨论了所生成的异斜体的一些稳定性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Arbitrarily large heteroclinic networks in fixed low-dimensional state space
We consider heteroclinic networks between n∈N nodes where the only connections are those linking each node to its two subsequent neighboring ones. Using a construction method where all nodes are placed in a single one-dimensional space and the connections lie in coordinate planes, we show that it is possible to robustly realize these networks in R6 for any number of nodes n using a polynomial vector field. This bound on the space dimension (while the number of nodes in the network goes to ∞) is a novel phenomenon and a step toward more efficient realization methods for given connection structures in terms of the required number of space dimensions. We briefly discuss some stability properties of the generated heteroclinic objects.
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