论文标题
加权网络中的同步和反同步
Synchrony and Anti-synchrony in Weighted Networks
论文作者
论文摘要
我们考虑了加权耦合的单元网络，即任何两个单元之间的相互作用具有相关的权重，这是一个实际有价值的数字。加权网络在实际应用中无处不在。我们通过将一个连续的动态系统（尊重网络的图形结构）关联来考虑动态系统的视角。对于加权网络，可允许的耦合细胞系统具有加性输入结构是很自然的。我们介绍了同步子空间和加权网络的反同步子空间的表征，具体取决于对其可允许的输入加添加性耦合细胞系统的限制。这些系统是这些系统的流动不变的，并且是通用的多二基因分空间，也就是说，以$ x_i = x_j $和/或$ x_k = -x_l $和/或$ x_l $和/或$ x_m = 0 $的细胞坐标的条件为特征。从应用和动力学的角度，加权网络的同步和反同步子空间的存在和识别与加权网络的存在非常相关。我们对加权网络的同步和反同步子空间的表征遵循我们的结果，在这些结果中，我们为广义多二基因与网络的laplacian矩阵提供了必要和足够的条件，以使其不变。
We consider weighted coupled cell networks, that is networks where the interactions between any two cells have an associated weight that is a real valued number. Weighted networks are ubiquitous in real-world applications. We consider a dynamical systems perspective by associating to each network a set of continuous dynamical systems, the ones that respect the graph structure of the network. For weighted networks it is natural for the admissible coupled cell systems to have an additive input structure. We present a characterization of the synchrony subspaces and the anti-synchrony subspaces for a weighted network depending on the restrictions that are imposed to their admissible input-additive coupled cell systems. These subspaces are flow-invariant by those systems and are generalized polydiagonal subspaces, that is, are characterized by conditions on the cell coordinates of the types $x_i = x_j$ and/or $x_k = -x_l$ and/or $x_m=0$. The existence and identification of the synchrony and anti-synchony subspaces for a weighted network are deeply relevant from the applications and dynamics point of view. Our characterization of the synchrony and anti-synchrony subspaces of a weighted network follows from our results where we give necessary and sufficient conditions for a generalized polydiagonal to be left invariant by the adjacency matrix and/or the Laplacian matrix of the network.
