网络上的模块化动力系统
Modular dynamical systems on networks
摘要：
我们提出了一个新的框架来研究网络上的连续时间动力系统。我们把这样的动力系统看作是相互作用的控制系统的集合。我们表明，一类图之间的映射称为图纤维化引起网络上的动力系统之间的映射。这使我们能够从组合数据中产生动力系统之间的共轭性。特别是，我们证明了满射图纤维化导致网络中的同步子空间。内射图纤维化，另一方面，产生从大动力系统到较小的满射映射。我们可以把这些满射看作是一种“快/慢”变量分解，或者是计算机科学意义上的“抽象”。
英文摘要：
We propose a new framework for the study of continuous time dynamical systems on networks. We view such dynamical systems as collections of interacting control systems. We show that a class of maps between graphs called graph fibrations give rise to maps between dynamical systems on networks. This allows us to produce conjugacy between dynamical systems out of combinatorial data. In particular we show that surjective graph fibrations lead to synchrony subspaces in networks. The injective graph fibrations, on the other hand, give rise to surjective maps from large dynamical systems to smaller ones. One can view these surjections as a kind of "fast/slow" variable decompositions or as "abstractions" in the computer science sense of the word.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
