An Overview of Synchrony in Coupled Cell Networks

Aguiar, Manuela A. D.; Dias, Ana Paula S.

doi:10.1007/978-3-319-74086-7_2

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2020

2021

Publication Types

Select...

Article1

Other1

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

(1 citation statement)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Coupled cell systems can be used to model a wide variety of phenomena in many scientific fields, ranging from physics, biology, chemistry, to engineering, social science and climatology (cf. Aguiar et al [3], Golubitsky et al [11] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Reduced Lattices of Synchrony Subspaces and Their Indices

Kamei¹,

Ruan

2021

SIAM J. Appl. Dyn. Syst.

View full text Add to dashboard Cite

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 non-negative integer index that leads to bifurcation analysis in regular coupled cell networks.

show abstract

Section: Introductionmentioning

confidence: 99%