Reduced lattices of synchrony subspaces and their indices

Hiroko Kamei, Haibo Ruan

Research output: Contribution to journalArticlepeer-review

Abstract

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 n-cell 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.

Original languageEnglish
Pages (from-to)636-670
Number of pages35
JournalSiam Journal on Applied Dynamical Systems
Volume20
Issue number2
Early online date8 Apr 2021
DOIs
Publication statusPublished - 2021

Keywords

  • Coupled cell network
  • Index
  • Jordan normal form
  • Lattice
  • Synchrony subspaces

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