The Library
Patterns of synchrony in coupled cell networks with multiple arrows
Tools
Golubitsky, Martin, Stewart, Ian and Torok, Andrei. (2005) Patterns of synchrony in coupled cell networks with multiple arrows. SIAM Journal on Applied Dymanical Systems, Vol.4 (No.1). pp. 78100. ISSN 15360040

PDF
WRAP_Stewart_10_1_1_77_4033_1.pdf  Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader Download (369Kb) 
Official URL: http://dx.doi.org/10.1137/040612634
Abstract
A coupled cell system is a network of dynamical systems, or “cells,” coupled together. The architecture
of a coupled cell network is a graph that indicates how cells are coupled and which cells are
equivalent. Stewart, Golubitsky, and Pivato presented a framework for coupled cell systems that
permits a classification of robust synchrony in terms of network architecture. They also studied
the existence of other robust dynamical patterns using a concept of quotient network. There are
two difficulties with their approach. First, there are examples of networks with robust patterns of
synchrony that are not included in their class of networks; and second, vector fields on the quotient
do not in general lift to vector fields on the original network, thus complicating genericity arguments.
We enlarge the class of coupled systems under consideration by allowing two cells to be coupled in
more than one way, and we show that this approach resolves both difficulties. The theory that we
develop, the “multiarrow formalism,” parallels that of Stewart, Golubitsky, and Pivato. In addition,
we prove that the pattern of synchrony generated by a hyperbolic equilibrium is rigid (the pattern
does not change under small admissible perturbations) if and only if the pattern corresponds to
a balanced equivalence relation. Finally, we use quotient networks to discuss Hopf bifurcation in
homogeneous cell systems with twocolor balanced equivalence relations.
Item Type:  Journal Article  

Subjects:  Q Science > QA Mathematics  
Divisions:  Faculty of Science > Mathematics  
Library of Congress Subject Headings (LCSH):  Coupled systems  
Journal or Publication Title:  SIAM Journal on Applied Dymanical Systems  
Publisher:  Society for Industrial and Applied Mathematics  
ISSN:  15360040  
Official Date:  22 February 2005  
Dates: 


Volume:  Vol.4  
Number:  No.1  
Page Range:  pp. 78100  
Identification Number:  10.1137/040612634  
Status:  Peer Reviewed  
Access rights to Published version:  Open Access  
Funder:  National Science Foundation (U.S.) (NSF), Norman Hackerman Advanced Research Program (NHARP)  
Grant number:  DMS0244529 (NSF), 00365200322001 (ARP)  
References:  [1] H. Brandt, ¨ Uber eine Verallgemeinerung des Gruppenbegriffes, Math. Ann., 96 (1927), pp. 360–366. 

URI:  http://wrap.warwick.ac.uk/id/eprint/183 
Request changes or add full text files to a record
Actions (login required)
View Item 
Downloads
Downloads per month over past year