Publisher DOI: 10.1137/20M1348832
Title: Reduced lattices of synchrony subspaces and their indices
Language: English
Authors: Kamei, Hiroko 
Ruan, Haibo  
Keywords: Coupled cell network; Index; Jordan normal form; Lattice; Synchrony subspaces
Issue Date: 8-Apr-2021
Publisher: SIAM
Source: SIAM Journal on Applied Dynamical Systems 20 (2): 636-670 (2021-04-08)
Abstract (english): 
For a regular coupled cell network, synchrony subspaces are the polydiagonal subspaces that are invariant under the network adjacency matrix. The complete lattice of synchrony subspaces of an ncell regular network can be seen as an intersection of the partition lattice of n elements and a lattice of invariant subspaces of the associated adjacency matrix. We assign integer tuples with synchrony subspaces and use them for identifying equivalent synchrony subspaces to be merged. Based on this equivalence, the initial lattice of synchrony subspaces can be reduced to a lattice of synchrony subspaces which corresponds to a simple eigenvalue case discussed in our previous work. The result is a reduced lattice of synchrony subspaces, which affords a well-defined nonnegative integer index that leads to bifurcation analysis in regular coupled cell networks.
ISSN: 1536-0040
Journal: SIAM journal on applied dynamical systems 
Institute: Mathematik E-10 
Document Type: Article
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