Networks


[with M.Golubitsky] Patterns of oscillation in coupled cell systems, in Geometry, Dynamics and Mechanics: 60th Birthday Volume for J.E. Marsden (eds. P.Holmes, P.Newton, and A.Weinstein), Springer-Verlag, New York 2002, 243-286.

[with M.Golubitsky and M.Pivato] Symmetry groupoids and patterns of synchrony in coupled cell networks, SIAM J. Appl. Dyn. Sys. 2 (2003) 609-646. [DOI: 10.1137/S1111111103419896; www.siam.org/journals/siads/x-x/41989.html]

Networking opportunity, Nature 427 (2004) 601-604.

[with M.Golubitsky and M.Nicol] Some curious phenomena in coupled cell networks, J. Nonlin. Sci. 14 (2004) 207-236.

[with A.P.S.Dias] Symmetry groupoids and admissible vector fields for coupled cell networks, J. London Math. Soc. (2) 69 (2004) 707-736.

[with M.Golubitsky and M.Pivato] Interior symmetry and local bifurcation in coupled cell networks, Dyn. Sys. 19 (2004) 389-407.

[with M.Golubitsky and A.Török] Patterns of synchrony in coupled cell networks with multiple arrows, SIAM J. Appl. Dyn. Sys. 4 (2005) 78-100. [DOI: 10.1137/040612634]

[with A.P.S.Dias] Linear equivalence and ODE-equivalence for coupled cell networks, Nonlinearity 18 (2005) 1003-1020.

[with M.Golubitsky] Synchrony versus symmetry in coupled cells, in: Equadiff 2003: Proceedings of the International Conference on Differential Equations, (eds. F.Dumortier, H.W.Broer, J.Mawhin, A.Vanderbauwhede, and S.M.Verduyn Lunel) World Scientific, Singapore 2005, 13-24.

[With F.A.M.Aldosray] Enumeration of homogeneous coupled cell networks, Internat. J. Bif. Chaos 15 (2005) 2361-2373.

[with M.Golubitsky] Nonlinear dynamics of networks: the groupoid formalism, Bull. Amer. Math. Soc. 43 (2006) 305-364.

[with F.Antoneli] Symmetry and synchrony in coupled cell networks 1: fixed-point spaces, Internat. J. Bif. Chaos 16 (2006) 559-577.

Elimination of multiple arrows and self-connections in coupled cell networks. Internat. J. Bif. Chaos 17 (2007) 99-106.

[with F.Antoneli] Symmetry and synchrony in coupled cell networks 2: group networks, Internat. J. Bif. Chaos 17 (2007) 935-951.

[with M.Golubitsky and L.J.Shiau] Spatio-temporal symmetries in the disynaptic canal-neck projection, SIAM J. Appl. Math. 67 (2007). [DOI: 10.1137/060667773]

The lattice of balanced equivalence relations of a coupled cell network, Math. Proc. Camb. Phil. Soc. 143 (2007) 165-183.

[with F.Antoneli] Symmetry and synchrony in coupled cell networks 3: exotic patterns, Internat. J. Bif. Chaos 18 (2008) 363-373.

[with M.Parker] Periodic dynamics of coupled cell networks I: rigid patterns of synchrony and phase relations, Dynamical Systems 22 (2007) 389-450.

[with M.Parker] Periodic dynamics of coupled cell networks II: cyclic symmetry, Dynamical Systems 23 (2008) 17-41.

[with M.Parker] A new mechanism for intermittency in rings of cells, Internat. J. Bif. Chaos 18 (2008) 675-687.