Invariant Synchrony and Anti-synchrony Subspaces of Weighted Networks

被引：2

作者：

Nijholt, Eddie ^{[1
]}

Sieben, Nandor ^{[2
]}

Swift, James W. W. ^{[2
]}

机构：

[1] Imperial Coll London, Dept Math, London, England

[2] No Arizona Univ, Dept Math & Stat, POB 5717, Flagstaff, AZ 86011 USA

来源：

JOURNAL OF NONLINEAR SCIENCE | 2023年 / 33卷 / 04期

基金：

瑞典研究理事会;

关键词：

Weighted coupled cell networks; Synchrony; Anti-synchrony; Invariant subspaces; INTERNAL SYMMETRY; COUPLED CELLS; ANTISYNCHRONY; DYNAMICS; PATTERNS; SYSTEMS;

D O I：

10.1007/s00332-023-09924-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The internal state of a cell in a coupled cell network is often described by an element of a vector space. Synchrony or anti-synchrony occurs when some of the cells are in the same or the opposite state. Subspaces of the state space containing cells in synchrony or anti-synchrony are called polydiagonal subspaces. We study the properties of several types of polydiagonal subspaces of weighted coupled cell networks. In particular, we count the number of such subspaces and study when they are dynamically invariant. Of special interest are the evenly tagged anti-synchrony subspaces in which the number of cells in a certain state is equal to the number of cells in the opposite state. Our main theorem shows that the dynamically invariant polydiagonal subspaces determined by certain types of couplings are either synchrony subspaces or evenly tagged anti-synchrony subspaces. A special case of this result confirms a conjecture about difference-coupled graph network systems.

引用

页数：38

共 38 条

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