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 30 (2020) 2930004.

[With M. Golubitsky, F. Antoneli, Z. Huang, and Y. Wang]  Input-output networks, singularity theory, and homeostasis, in  Advances in Dynamics, Optimzation and Computation (eds. O. Junge, O. Schütze, G. Froyland, S. Ober-Blöbaum, and K. Padberg-Gehle), Studies in Systems, Decision and Control 304,Springer, Berlin 2020, 31–65.

Overdetermined constraints and rigid synchrony patterns for network equilibria, Portugaliae Mathematica 77 (2020) 163–196.

Finite characterization of the coarsest balanced coloring of a network, Internat. J. Bif. Chaos to appear.