Biomathematics

[with J.J.Collins] Symmetry-breaking bifurcation: a possible mechanism for 2:1 frequency-locking in animal locomotion, J. Math. Biol. 30 (1992) 827-838.

[with J.J.Collins] Hexapodal gaits and coupled nonlinear oscillator models, Biol. Cybern. 68 (1993) 287-298.

[with J.J.Collins] Coupled nonlinear oscillators and the symmetries of animal gaits, J. Nonlin. Sci. 3 (1993) 349-392.

[with P.Bromwich, J.Cohen, and A.Walker] Decline in sperm counts: an artefact of changed reference range of "normal"? British Medical Journal 309 (2 July 1994) 19-22. Reprinted (abbreviated) in Yearbook of Infertility 1995 (ed. R.Z.Sokol), Mosby, Chicago IL 1995.

[with J J Collins] A group-theoretic approach to rings of coupled biological oscillators, Biol. Cybern. 71 (1994) 95-103.

[with P.Bromwich, J.Cohen, and A.Walker] Decline in sperm counts: an artefact of changed reference range of "normal"? [abbreviated and supplemented version], Fertility Digest (1995).

[with J.J.Collins, M.Golubitsky, and L.Buono] A modular network for legged locomotion, Physica D 115 (1998) 56-72.

[with M.Golubitsky, J.J.Collins, and P.-L.Buono] Symmetry in locomotor central pattern generators and animal gaits, Nature 401 (1999) 693-695.

[with J.Cohen] Polymorphism viewed as phenotypic symmetry-breaking, in Nonlinear Phenomena in Biological and Physical Sciences (eds. S.K.Malik, M.K.Chandrasekharan, and N.Pradhan), Indian National Science Academy, New Delhi 2000, 1-63.

Designer differential equations for animal locomotion, Complexity 5 no.2 (2000) 12-22.

Ruptura de la simetria, formació de patrons i caos simètric en sistemes dinàmics no lineals (Symmetry-breaking, pattern formation, and symmetric chaos in nonlinear dynamical systems), Butlletí Soc. Catalana Mat. 17 (2002) 123-141.

[with T.Elmhirst and J.Cohen] Symmetry-breaking as an origin of species, in Bifurcations, Symmetry, and Patterns (eds. J. Buescu, S. Castro, A.P.S. Dias, and I. Labouriau), Birkhäuser, Basel 2003, 3-54.

Broken symmetries and biological patterns, in On Growth, Form, and Computers (eds. S.Kumar and P.J.Bentley), Elsevier, London 2003, 181-202.

Speciation: a case study in symmetric bifurcation theory, Univ. Iagellonicae Acta Math. 41 (2003) 67-88.

Self-organization in evolution: a mathematical perspective, Nobel Symposium Proceedings, Phil. Trans. Roy. Soc. Lond. A 361 (2003) 1101-1123.

[with A.Price and M.Keeling] A robustness metric integrating spatial and temporal information: application to coral reefs exposed to local and regional disturbances, Marine Ecology Progress Series 331 (2007) 101-108.

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

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

[with T.Elmhirst and M.Doebeli] Pod systems: an equivariant ordinary differential equation approach to dynamical systems on a spatial domain, Nonlinearity 24 (2008) 1507-1531.

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, SIADS, to appear.

[with M. Golubitsky] Symmetry methods in mathematical biology, São Paulo J. Math. Sci. 9 (2015) 1-36.

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

[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.

[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.

[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 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.

Symmetry and network architecture in neuronal circuits: Complicity of form and function, Internat. J. Bif. Chaos 32 (2022) 2230033;
            doi:10.1142/S0218127422300336.