Symmetry and synchrony in coupled cell networks 2: Group networks

International Journal of Bifurcation and Chaos

Volumn 17, Issue 3, 2007, Pages 935-951

  Antoneli, Fernando ^a   Stewart, Ian ^b  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

^b UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

Network dynamics; Symmetry; Synchrony

Indexed keywords

ALGEBRA; COMPUTATIONAL METHODS; COMPUTER ARCHITECTURE; NETWORK MANAGEMENT; SYNCHRONIZATION;

AUTOMORPHISM; NETWORK DYNAMICS; PERMUTATION; SYMMETRY; SYNCHRONY;

NETWORK ARCHITECTURE;

EID: 34249006867     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127407017641     Document Type: Article

References (16)

1. Antoneli, F., Dias, A. P. S., Golubitsky, M. & Wang, Y. [2005] "Patterns of synchrony in lattice dynamical systems," Nonlinearity 18, 2193-2209.
2. Antoneli, F. & Stewart, I. [2006] "Symmetry and synchrony in coupled cell networks 1: fixed-point spaces, Int. J. Bifurcation and Chaos 16, 559-577.
3. Conway, J. H., Curtis, R. T., Norton, S., Parker, R. A. & Wilson, R. A. [1985] Atlas of Finite Groups (Cambridge University Press, Cambridge); Reprinted with corrections and additions [2003].
4. Davey, B. A. & Priestley, H. A. [1990] Introduction to Lattices and Order (Cambridge University Press Cambridge).
5. Golubitsky, M. & Stewart, I. [2002] The Symmetry Perspective: From Equilibrium to Chaos in Phase Space and Physical Space, Progress in Mathematics, Vol. 200 (Birkhäuser, Basel).
6. Gorenstein, D. [1968] Finite Groups (Harper & Row, NY).
7. Gray, J. J. [1982] "From the history of a simple group," Math. Intelligencer 4, 59-67;
8. also in Levy, S. (ed.) [1999] The Eightfold Way: The Beauty of Klein's Quartic Curve, MSRI Publications (Berkeley and Cambridge University Press), pp. 115-131.
9. Hahn, T. [1992] International Tables for Crystallography: Volume A, Space-group Symmetry (Kluwer, Dordrecht).
10. Hall, M. Jr. [1959] The Theory of Groups (Macmillan, NY).
11. Klein, C. F. [1879] "Über die transformation siebenter Ordnung der elliptischen funktionen," Math. Ann. 14 (= Ges. Math. Abh. III) 90-134.
12. Neumann, P. M. Stoy, G. A. & Thompson, E. C. [1994] Groups and Geometry (Oxford University Press, Oxford).
13. Stewart, I. Golubitsky, M. & Pivato. M. [2003] "Patterns of synchrony in coupled cell networks," SIAM J. Appl. Dyn. Syst. 2, 609-646.
14. Tutte, W. T. [1984] Graph Theory, Encyclopaedia of Mathematics and Its Applications, ed. Rota, G.-C., Vol. 21 (Addison-Wesley, Menlo Park).
15. Wang, Y. and Golubitsky, M. [2005] "Two-color patterns of synchrony in lattice dynamical systems," Nonlinearity 18, 631-657.
16. Wilson, R. J. [1985] Introduction to Graph Theory, 3rd edition (Longman, Harlow).