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.

Pod systems: an equivariant ordinary differential equation approach to dynamical systems on a spatial domain, Nonlinearity 24 (2008) 1507-1531.

[with M. Parker and MGM Gomes] Examples of forced symmetry-breaking to heteroclinic cycles and networks in three-dimensional Euclidean-invariant systems, Internat. J. Bif. Chaos 19 (2009) 1655-1678.

An optimal lifting theorem for coupled cell networks, Internat. J. Bif. Chaos  21 (2011) 2481-2487.

[with M. Golubitsky] Synchrony-breaking bifurcations at a simple real eigenvalue for regular networks 1: 1-dimensional cells, SIAM J. Appl. Dyn. Sys. 10 (2011) 1404-1442. [DOI: 10.1137/110825418]

Symmetry-breaking in a rate model for a biped locomotion central pattern generator. Special issue on symmetry-breaking, Symmetry 6 (2014) 23-66;
    doi:10.3390/sym6010023.

Synchrony-breaking bifurcations at a simple real eigenvalue for regular networks 2: higher-dimensional cells, SIAM J. Appl. Dyn. Sys. 13 (2014) 129–156. [DOI: 10.1137/130917636]

[with M. Golubitsky] Recent advances in symmetric and network dynamics, Chaos 25, 097612 (2015); DOI: 10.1063/1.4918595.

[with M. Golubitsky] Homeostasis, singularities, and networks, Journal of Mathematical Biology (2016) DOI 10.1007/s00285-016-1024-2.

[with M. Golubitsky] Rigid patterns of synchrony for equilibria and periodic cycles in network dynamics, Chaos 26 (2016) 094803; doi: 10.1063/1.4953664.

A formal setting for network dynamics, in: Complex Networks and Dynamics (ed. P.Commendatore, M. Matilla-García, L.M. Varela, and J.S. Cánovas), Springer, to appear 2016. Lecture Notes in Economics and Mathematical Systems 683, 239–266. DOI 10.1007/978-3-319-40803-3_10.

[with M. Golubitsky] Coordinate changes that preserve admissible maps for network dynamics, Dynamical Systems 32 (2017) 81–116. [Equivariance and Beyond: M. Golubitsky’s 70th Birthday.] DOI: 10.1080/14689367.2016.1235136.

[with M. Reed, J.Best, M. Golubitsky, and F. Nijhout] Analysis of homeostatic mechanisms in biochemical networks, Bull Math. Biology (2017) 79 2534-2557. DOI: 10.1007/s11538-017-0340-z.

Spontaneous symmetry-breaking in a network model for quadruped locomotion. Internat. J. Bif. Chaos 27 (2017) 1730049 [25 pages].

[with M. Golubitsky] Homeostasis with multiple inputs, SIAM J. Applied Dynamical Systems 17 (2018) 1816–1832.

[with F. Antoneli and M. Golubitsky] Homeostasis in a feed forward loop gene regulatory network motif, J. Theoret. Biol. 445 103–109;
            DOI: 10.1016/j.jtbi.2018.02.026.

Exotic patterns of synchrony in planar lattice networks, Internat. J. Bif. Chaos 29 (2019) 1939993 [23 pages].

[with M. Golubitsky] Symmetric networks with geometric constraints as models of visual illusions. Symmetry [special issue on Symmetry and Dynamical Systems] 11 (2019), 799; doi:10.3390/sym11060799.

[With D. Gökaydin] Symmetries of quotient networks for doubly periodic patterns on the square lattice,  Internat. J. Bif. Chaos 29 (2019);
            doi: 10.1142/S021812741930026X.

[with P. Gandhi, M. Golubitsky, C. Postlethwaite, and Y. Wang] Bifurcations on fully inhomogeneous networks, SIADS, to appear.

[With D. Gökaydin] Symmetries of quotient networks for doubly periodic patterns on the hexagonal lattice, Internat. J. Bif. Chaos, to appear.