Publisher DOI: 10.1142/S0218127421500735
Title: Hidden symmetries, coupled networks and equivariant degrees
Language: English
Authors: Ruan, Haibo  
Keywords: Symmetry; coupled network; equivariant degree; synchrony-breaking bifurcation
Issue Date: Apr-2021
Publisher: World Scientific
Source: International journal of bifurcation and chaos (IJBC) 31 (5): 2150073 (2021-04)
Abstract (english): 
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
Journal: International journal of bifurcation and chaos (IJBC) 
Institute: Mathematik E-10 
Document Type: Article
Peer Reviewed: Yes
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