论文标题
加权网络的不变同步和反同步子空间
Invariant Synchrony and Anti-Synchrony Subspaces of Weighted Networks
论文作者
论文摘要
耦合细胞网络中单元格的内部状态通常由向量空间的元素描述。当某些细胞处于相同状态或相反状态时，会同步或反同步。在同步或反同步中包含细胞的状态空间的子空间称为聚二基因子空间。我们研究了加权耦合细胞网络的几种类型的聚二元子空间的性能。特别是，我们计算此类子空间的数量并在动态不变时进行研究。特别感兴趣的是均匀标记的反同步子空间，其中特定状态的细胞数量等于相反状态的细胞数量。我们的主要定理表明，由某些类型的耦合确定的动态不变的多二基因子空间要么是同步子空间或均匀标记的反同步子空间。此结果的一种特殊情况证实了关于差耦合图网络系统的猜想。
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.
