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Hidden symmetries, coupled networks and equivariant degrees
Publikationstyp
Journal Article
Date Issued
2021-04
Sprache
English
Author(s)
Ruan, Haibo
Institut
TORE-URI
Volume
31
Issue
5
Article Number
2150073
Citation
International journal of bifurcation and chaos (IJBC) 31 (5): 2150073 (2021-04)
Publisher DOI
Scopus ID
Publisher
World Scientific
Peer Reviewed
true
Hidden symmetries have been previously explored in the context of coupled cell networks and coupled cell systems. These include interior symmetry, quotient symmetry and quotient interior symmetry. We introduce here an equivariant degree theory that incorporates these different forms of hidden symmetry based on lattice structures of synchrony subspaces. The result is a unified theory capable of treating synchrony-breaking Hopf bifurcation problems in coupled cell systems with various forms of hidden symmetries, which leads to full topological classifications of bifurcating branches arising from single bifurcation points under mutual influence of these hidden symmetries.
© 2021 World Scientific Publishing Co Pte Ltd
© 2021 World Scientific Publishing Co Pte Ltd
Subjects
Symmetry
coupled network
equivariant degree
synchrony-breaking bifurcation
DDC Class
510: Mathematik