Reduced lattices of synchrony subspaces and their indices

Publikationstyp
Journal Article
Date Issued
2021-04-08
Sprache
English
Author(s)
Kamei, Hiroko  
Ruan, Haibo 
Institut
Mathematik E-10  
TORE-URI
http://hdl.handle.net/11420/9548
Journal
SIAM journal on applied dynamical systems  
Volume
20
Issue
2
Start Page
636
End Page
670
Citation
SIAM Journal on Applied Dynamical Systems 20 (2): 636-670 (2021-04-08)
Publisher DOI
10.1137/20M1348832
Scopus ID
2-s2.0-85105341464
Publisher
SIAM
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.
Subjects
Coupled cell network
Index
Jordan normal form
Lattice
Synchrony subspaces
DDC Class
004: Informatik
510: Mathematik