• M. Golubitsky and I. Stewart. Dynamics and Bifurcation in Networks: Theory and Application of Coupled Differential Equations. SIAM, 2023,
• Z. Huang and M. Golubitsky. Classification of infinitesimal homeostasis in four-node input-output networks. J. Math. Biology. 84 (2022) 62. [Abstract] [PDF 368K]
• M. Golubitsky, I. Stewart, F. Antoneli, Z. Huang and YY. Wang. Input-output networks, singularity theory, and homeostasis. In: Proceedings on the Workshop of Dynamics, Optimization, and Computation. (O. Junge, S. Ober-Blobaum, K. Padburg-Gehle,G. Froyland, and O. Schütze, eds.) Springer Nature Switzerland AG, 2021, [Abstract] [PDF 1.6M]
• YY. Wang, Z. Huang, F. Antoneli and M. Golubitsky. The structure of infinitesimal homeostasis in input-output networks. J. Math. Biol. 82 (2021) https://doi.org/10.1007/s00285-021-01614-1 [Abstract] [PDF 496K]
• P. Gandhi, M. Golubitsky, C. Postlethwaite, I. Stewart and YY. Wang. Bifurcations on fully inhomogeneous networks. SIAM J. Appl. Dynam. Sys. (2020) 366-411. [Abstract] [PDF 2.0M]
• M. Golubitsky and YY. Wang. Infinitesimal homeostasis in three-node input-output networks. J. Math. Biol. (2020) 1163-1185 doi: 10.1007/s00285-019-01457-x [Abstract] [PDF 733K]
• W. Duncan and M. Golubitsky. Coincidence of homeostasis and bifurcation in feedforward networks. Intern. J. Bif. Chaos. (2019) 1930037-1-29; DOI:10.1142/S0218127419300374 [Abstract] [PDF 3.5M]
• M. Golubitsky, Y. Zhao, YJ. Wang and Z-L. Lu. The symmetry of generalized rivalry network models determines patterns of interocular grouping in four-location binocular rivalry. J. Neurophysiology. (2019) 1989-1999. [Abstract] [PDF 786K]
• I. Stewart and M. Golubitsky. Symmetric networks with geometric constraints as models of visual illusions. Symmetry. 11(6) (2019) 799; http://dx.doi.org/10.3390/sym11060799 [Abstract] [PDF 8.6M]
• F. Antoneli, M. Golubitsky and I. Stewart. Homeostasis in a feed forward loop gene regulatory network motif. J. Theoretical Biology. 445 (2018) 103-109; DOI:10.1016/j.jtbi.2018.02.026 [Abstract] [PDF 779K]
• W. Duncan, J. Best, M. Golubitsky, H.F. Nijhout and M. Reed. Homeostasis despite instability. Math. Biosci. 300 (2018) 130-137. doi: 10.1016/j.mbs.2018.03.025 [Abstract] [PDF 1.0M]
• M. Golubitsky and I. Stewart. Homeostasis with multiple inputs. SIAM J. Appl. Dynam. Sys. 17 (2) (2018) 1816-1832. [Abstract] [PDF 2.7M]
• M. Golubitsky, W. Hao, K-Y. Lam and Y. Lou. Dimorphism by singularity theory in a model for river ecology. Bull. Math. Biol. 79(5) (2017) 1051-1069; DOI 10.1007/s11538-017-0268-3 [Abstract] [PDF 1.3M]
• M. Golubitsky and I. Stewart. Coordinate changes for network dynamics. Dynamical Systems. 32 (2017) 80-116; DOI 10.1080/14689367.2016.1235136 [Abstract] [PDF 902K]
• M. Golubitsky and I. Stewart. Homeostasis, singularities and networks. J. Mathematical Biology. 74 (2017) 387-407 DOI 10.1007/s00285-016-1024-2 [Abstract] [PDF 853K]
• M. Reed, J. Best, M. Golubitsky, I. Stewart and H.F. Nijhout. Analysis of homeostatic mechanisms in biochemical networks. Bull. Math. Biol. 79(9) (2017) 1-24; DOI: 10.1007/s11538-017-0340-z [Abstract] [PDF 1.9M]
• M. Golubitsky, L. Matamba Messi and L.E. Spardy. Symmetry types and phase-shift synchrony in networks. Physica D. 320 (2016) 9-18. [Abstract] [PDF 478K]
• M. Golubitsky and I. Stewart. Rigid patterns of synchrony for equilibria and periodic cycles in network dynamics. Chaos. 26 (2016) 094803; DOI 10.1063/1.4953664 [Abstract] [PDF 979K]
• X. Wang and M. Golubitsky. Singularity theory of fitness functions under dimorphism equivalence. J. Mathematical Biology. 73(3) (2016) 525-573 10.1007/s00285-015-0958-0 [Abstract] [PDF 1.8M]
• M. Golubitsky and I. Stewart. Recent advances in symmetric and network dynamics. Chaos. 25 (2015) 097612 DOI: 10.1063/1.4918595 [Abstract] [PDF 1.8M]
• M. Golubitsky and I. Stewart. Symmetry methods in mathematical biology. Sao Paulo J. Math. Sciences. 9 (2015) 1-36. [Abstract] [PDF 1.7M]
• J. Wiser and M. Golubitsky. Bifurcations in forced response curves. SIAM J. Appl. Dynam. Sys. 14 (4) (2015) 2013-2026. [Abstract] [PDF 1.7M]
• C. Diekman and M. Golubitsky. Network symmetry and binocular rivalry experiments. J. Math. Neuro. 4 (12) (2014) DOI 10.1186/2190-8567-4-12 [Abstract] [PDF 1.3M]
• A. Vutha and M. Golubitsky. Normal forms and unfoldings of singular strategy functions. Dynam. Games & Appl. 5 (2) (2014) 180-213. [Abstract] [PDF 1.2M]
• C. Diekman, M. Golubitsky and YJ. Wang. Derived patterns in binocular rivalry networks. J. Math. Neuro. 3 (6) (2013) doi:10.1186/2190-8567-3-6 [Abstract] [PDF 1.1M]
• M. Golubitsky. Patterns in physical and biological systems. In: Models, Simulations, and the Reduction of Complexity. (U. Gahde, S. Hartmann, J.H. Wolf, ed.) de Gruyter GmbH, Berlin, 2013, 29-42. [PDF 4.7M]
• C. Diekman, M. Golubitsky, T. McMillen and YJ. Wang. Reduction and dynamics of a generalized rivalry network with two learned patterns. SIAM J. Appl. Dynam. Sys. 11 (4) (2012) 1270-1309. [Abstract] [PDF 1.2M]
• M. Golubitsky and C. Postlethwaite. Feed-forward networks, center manifolds, and forcing. Discrete and Continuous Dynamical Systems - Series A. 32 (2012) 2913-2935. [Abstract] [PDF 541K]
• M. Golubitsky, D. Romano and YJ. Wang. Network periodic solutions: patterns of phase-shift synchrony. Nonlinearity. 25 (2012) 1045-1074. [Abstract] [PDF 480K]
• I. Stewart and M. Golubitsky. Synchrony-breaking bifurcation at a simple real eigenvalue for regular networks 1:1-dimensional cells. SIAM J. Appl. Dynam. Sys. 10 (4) (2011) 1404-1442. [Abstract] [PDF 428K]
• Y. Zhang and M. Golubitsky. Periodically forced Hopf bifurcation. SIAM J. Appl. Dynam. Sys. 10 (2011) 1272-1306. [Abstract] [PDF 803K]
• N. Filipski and M. Golubitsky. The abelian Hopf H mod K theorem. SIAM J. Appl. Dynam. Sys. 9 (2) (2010) 283-291. [Abstract] [PDF 198K]
• M. Golubitsky, D. Romano and YJ. Wang. Network periodic solutions: full oscillation and rigid synchrony. Nonlinearity. 23 (2010) 3227-3243. [Abstract] [PDF 202K]
• M.A.D. Aguiar, A.P.S. Dias, M. Golubitsky and M.C.A. Leite. Bifurcations from regular quotient networks: A first insight. Physica D. 238 (2) (2009) 137-155. [Abstract] [PDF 1.4M]
• M. Golubitsky and R. Lauterbach. Bifurcations from synchrony in homogeneous networks: linear theory. SIAM J. Appl. Dynam. Sys. 8 (1) (2009) 40-75. [Abstract] [PDF 482K]
• M. Golubitsky, C. Postlethwaite, L-J. Shiau and Y. Zhang. The feed-forward chain as a filter amplifier motif. In: Coherent Behavior in Neuronal Networks. (K. Josic, M. Matias, R. Romo, and J. Rubin, eds.) Springer, 2009, 95-120. [Abstract] [PDF 594K]
• A. Comanici and M. Golubitsky. Patterns on growing square domains via mode interactions. Dynamical Systems. 23, No.2 (2008) 167-206. [Abstract] [PDF 442K]
• M.A.D. Aguiar, A.P.S. Dias, M. Golubitsky and M.C.A. Leite. Homogeneous coupled cell networks with S_3-symmetric quotient. Discrete and Continuous Dynam. Sys. Supplement (2007) 1-9. [Abstract] [PDF 205K]
• F. Antoneli, A.P.S. Dias, M. Golubitsky and YJ. Wang. Synchrony in lattice differential equations. In: Some Topics In Industrial and Applied Mathematics. (R. Jeltsch, T. Li, and I. Sloan, eds.) Contemporary Applied Mathematics Series 8 World Scientific Publ. Co., 2007, [Abstract] [PDF 341K]
• H.W. Broer, M. Golubitsky and G. Vegter. The geometry of resonance tongues. In: Singularity Theory. (D. Cheniot, N. Dutertre, C. Murolo, D. Trotman and A. Pichon, eds.) World Scientific Publ. Co., 2007, 327-356. [Abstract] [PDF 442K]
• M. Golubitsky and M. Krupa. Stability computations for nilpotent Hopf bifurcations in coupled cell systems. International Journal of Bifurcation and Chaos. 17 (2007) 2595-2603. [Abstract] [PDF 410K]
• M. Golubitsky, L-J. Shiau and I. Stewart. Spatiotemporal symmetries in the disynaptic canal-neck projection. SIAM J Appl Math. 67 (5) (2007) 1396-1417. [Abstract] [PDF 218K]
• N.J. McCullen, T. Mullin and M. Golubitsky. Sensitive signal detection using a feed-forward oscillator network. Phys. Rev. Lett. 98 (2007) 254101. [Abstract] [PDF 246K]
• F. Antoneli, A.P.S. Dias, M. Golubitsky and YJ. Wang. Flow invariant subspaces for lattice dynamical systems. In: Bifurcation Theory and Spatio-Temporal Pattern Formation. (W. Nagata and N.S. Namachchivaya, eds.) Fields Institute Communications, 2006, 1-8. [Abstract] [PDF 172K]
• T. Elmhirst and M. Golubitsky. Nilpotent Hopf bifurcations in coupled cell systems. SIAM J. Appl. Dynam. Sys. 5 (2006) 205-251. [Abstract] [PDF 489K]
• M. Golubitsky. Symmetry and Neuroscience. Current Events, Amer. Math. Soc. January 14 (2006) [Abstract] [PDF 700K]
• M. Golubitsky, K. Josic and E. Shea-Brown. Winding numbers and averaged frequencies in phase oscillator networks. J. Nonlinear Science. 16 (2006) 201-231. [Abstract] [PDF 2.4M]
• M. Golubitsky and I. Stewart. Nonlinear dynamics of networks: the groupoid formalism. Bull. Amer. Math. Soc. 43 (2006) 305-364. [Abstract] [PDF 2.4M]
• M.C.A. Leite and M. Golubitsky. Homogeneous three-cell networks. Nonlinearity. 19 (2006) 2313-2363. [Abstract] [PDF 497K]
• C.A. Pinto and M. Golubitsky. Central pattern generators for bipedal locomotion. J. Math. Biol. 53 (2006) 474-489. [Abstract] [PDF 189K]
• F. Antoneli, A.P.S. Dias, M. Golubitsky and YJ. Wang. Patterns of synchrony in lattice dynamical systems. Nonlinearity. 18 (2005) 2193-2209. [Abstract] [PDF 396K]
• M. Golubitsky, K. Josic and L-J. Shiau. Bursting in coupled cell systems. In: Bursting: The Genesis of Rhythm in the Nervous System. (S. Coombes and P.C. Bressloff, eds.) World Scientific Publ. Co., 2005, 205-225. [Abstract] [PDF 642K]
• M. Golubitsky and I. Stewart. Synchrony versus symmetry in coupled cells. In: Equadiff 2003: Proceedings of the International Conference on Differential Equations. (F. Dumortier, H.W. Broer, J. Mawhin, A. Vanderbauwhede and S.M. Verduyn Lunel, eds.) World Scientific Publ. Co., Singapore, 2005, 13-24. [Abstract] [PDF 643K]
• M. Golubitsky, I. Stewart and A. Torok. Patterns of synchrony in coupled cell networks with multiple arrows. SIAM J. Appl. Dynam. Sys. 4 (1) (2005) 78-100. [Abstract] [PDF 363K]
• YJ. Wang and M. Golubitsky. Two-color patterns of synchrony in lattice dynamical systems: complete. University of Houston preprint. (2005) [Abstract] [PDF 923K]
• YJ. Wang and M. Golubitsky. Two-color patterns of synchrony in lattice dynamical systems. Nonlinearity. 18 (2005) 631-657. [Abstract] [PDF 711K]
• M. Golubitsky, M. Nicol and I. Stewart. Some curious phenomena in coupled cell systems. J. Nonlinear Sci. 14 (2) (2004) 207-236. [Abstract] [PDF 1.3M]
• M. Golubitsky, M. Pivato and I. Stewart. Interior symmetry and local bifurcation in coupled cell networks. Dynamical Systems. 19 (4) (2004) 389-407. [Abstract] [PDF 418K]
• M. Golubitsky, L-J. Shiau and A. Torok. Symmetry and pattern formation on the visual cortex. In: Dynamics and Bifurcation of Patterns in Dissipative Systems. (G. Danglmayer and J. Opera, eds.) Series on Nonlinear Science 12 World Scientific Publishing Co., Singapore, 2004, 3-19. [Abstract] [PDF 467K]
• H.W. Broer, M. Golubitsky and G. Vegter. The geometry of resonance tongues: a singularity theory approach. Nonlinearity. 16 (2003) 1511-1538. [Abstract] [PDF 433K]
• D. Chillingworth and M. Golubitsky. Symmetry and pattern formation for a planar layer of nematic liquid crystal. Journal of Mathematical Physics. 44 (9) (2003) 4201-4219. [Abstract] [PDF 581K]
• M. Golubitsky and D. Chillingworth. Bifurcation and planar pattern formation for a liquid crystal. In: Conference on Bifurcations, Symmetry and Patterns. (J. Buescu, S. Castro, A. Dias and I. Labouriau, eds.) Birkhauser, Basel, 2003, 55-66. [Abstract] [PDF 650K]
• M. Golubitsky, L-J. Shiau and A. Torok. Bifurcation on the visual cortex with weakly anisotropic lateral coupling. SIAM J. Appl. Dynam. Sys. 2 (2003) 97-143. [Abstract] [PDF 10.2M]
• I. Stewart, M. Golubitsky and M. Pivato. Symmetry groupoids and patterns of synchrony in coupled cell networks. SIAM J. Appl. Dynam. Sys. 2 (4) (2003) 609-646. [Abstract] [PDF 2.3M]
• P.C. Bressloff, J.D. Cowan, M. Golubitsky, P.J. Thomas and M.C. Wiener. What geometric visual hallucinations tell us about the visual cortex. Neural Computation. 14 (2002) 473-491. [Abstract] [PDF 1.8M]
• M. Golubitsky and P.H. Rabinowitz. A sketch of the Hopf bifurcation theorem. In: Selected Works of Eberhard Hopf with Commentaries. (C.S. Morawetz, J.B. Serrin and Y.G. Sinai, eds.) Amer. Math. Soc., Providence, 2002, 111-118. [PDF 137K]
• M. Golubitsky and I. Stewart. Patterns of oscillation in coupled cell systems. In: Geometry, Dynamics, and Mechanics: 60th Birthday Volume for J.E. Marsden. (P. Holmes, P. Newton and A. Weinstein, eds.) Springer-Verlag, 2002, 243-286. [Abstract] [PDF 2.6M]
• M. Golubitsky and I. Stewart. The Symmetry Perspective: From Equilibrium to Chaos in Phase Space and Physical Space. Birkhauser, 2002, (Translated into: Japanese)
• P.C. Bressloff, J.D. Cowan, M. Golubitsky and P.J. Thomas. Scalar and pseudoscalar bifurcations motivated by pattern formation on the visual cortex. Nonlinearity. 14 (2001) 739-775. [Abstract] [PDF 998K]
• P.C. Bressloff, J.D. Cowan, M. Golubitsky, P.J. Thomas and M.C. Wiener. Geometric visual hallucinations, Euclidean symmetry, and the functional architecture of striate cortex. Phil. Trans. Royal Soc. London B. 356 (2001) 299-330. [Abstract] [PDF 4.4M]
• P.L. Buono and M. Golubitsky. Models of central pattern generators for quadruped locomotion: I. primary gaits. J. Math. Biol. 42 (4) (2001) 291-326. [Abstract] [PDF 514K]
• M. Golubitsky, K. Josic and T.J. Kaper. An unfolding theory approach to bursting in fast-slow systems. In: Global Analysis of Dynamical Systems: Festschrift dedicated to Floris Takens on the occasion of his 60th birthday. (H.W. Broer, B. Krauskopf and G. Vegter, eds.) Institute of Physics Publ., 2001, 277-308. [Abstract] [PDF 2.5M]
• M. Golubitsky and I. Melbourne. A symmetry classification of columns. Visual Mathematics. 3 (1) (2001) [Abstract] [PDF 1.3M]
• D. Barkley, L.S. Tuckerman and M. Golubitsky. Bifurcation theory for three-dimensional flow in the wake of a circular cylinder. Phys. Rev. E. 61 (5) (2000) 5247-5252. [Abstract] [PDF 70K]
• P.L. Buono, M. Golubitsky and A. Palacios. Heteroclinic cycles in rings of coupled cells. Physica D. 143 (2000) 74-108. [Abstract] [PDF 962K]
• M. Golubitsky, E. Knobloch and I. Stewart. Target patterns and spirals in planar reaction-diffusion systems. J. Nonlinear Sci. 10 (2000) 333-354. [Abstract] [PDF 1.0M]
• M. Golubitsky, V.G. LeBlanc and I. Melbourne. Hopf bifurcation from rotating waves and patterns in physical space. J. Nonlin. Sci. 10 (2000) 69-101. [Abstract] [PDF 331K]
• P.L. Buono, M. Golubitsky and A. Palacios. Heteroclinic cycles in systems with D_n symmetry. In: Bifurcation Theory and its Numerical Analysis. (Z. Chen, S-N Chow and K. Li, eds.) Springer-Verlag Singapore Pte. Ltd., 1999, 13-27. [Abstract] [PDF 1.1M]
• M. Golubitsky and M. Dellnitz. Linear Algebra and Differential Equations Using MATLAB. Brooks-Cole Publishers, 1999, (Translated into: Spanish)
• M. Golubitsky and I. Stewart. Symmetry and pattern formation in coupled cell networks. In: Pattern Formation in Continuous and Coupled Systems. (M. Golubitsky, D. Luss and S.H. Strogatz, eds.) IMA Volumes in Mathematics and its Applications 115 Springer, New York, 1999, 65-82. [Abstract] [PDF 952K]
• M. Golubitsky, I. Stewart, P.L. Buono and J.J. Collins. Symmetry in locomotor central pattern generators and animal gaits. Nature. 401 (1999) 693-695. [Abstract] [PDF 153K]
• C.N. Jensen, M. Golubitsky and H. True. Symmetry, generic bifurcations, and mode interaction in nonlinear railway dynamics. International Journal of Bifurcation and Chaos. 9 (7) (1999) 1321-1331. [Abstract] [PDF 461K]
• C.N. Jensen, M. Golubitsky and H. True. Symmetry, generic bifurcations, and mode interaction in nonlinear railway dynamics. In: IUTAM Symposium on New Applications of Nonlinear and Chaotic Dynamics in Mechanics. (F.C. Moon, ed.) Kluwer Acad. Publ., 1999, 387-396. [Abstract]
• M. Golubitsky and I. Melbourne. A symmetry classification of columns. In: Bridges: Mathematical Connections in Art, Music, and Science. (Reza Sarhangi, ed.) 1998 Bridges Conference, 1998, 209-223. [Abstract] [PDF 1.2M]
• M. Golubitsky, I. Stewart, P.L. Buono and J.J. Collins. A modular network for legged locomotion. Physica D. 115 (1998) 56-72. [Abstract] [PDF 1.1M]
• D. Gillis and M. Golubitsky. Patterns in square arrays of coupled cells. JMAA. 208 (1997) 487-509. [Abstract] [PDF 462K]
• D. Gillis and M. Golubitsky. An algorithm for symmetry detectives. Physica D. 107 (1997) 23-29. [Abstract] [PDF 285K]
• M. Golubitsky, V.G. LeBlanc and I. Melbourne. Meandering of the spiral tip: An alternative approach. J. Nonlin. Sci. 7 (6) (1997) 555-586. [Abstract] [PDF 451K]
• C. Hou and M. Golubitsky. An example of symmetry breaking to heteroclinic cycles. J. Diff. Eqn. 133 (1) (1997) 30-48. [Abstract] [PDF 407K]
• B. Dionne, M. Golubitsky and I. Stewart. Coupled cells with internal symmetry Part I: wreath products. Nonlinearity. 9 (1996) 559-574. [Abstract] [PDF 216K]
• B. Dionne, M. Golubitsky and I. Stewart. Coupled cells with internal symmetry Part II: direct products. Nonlinearity. 9 (1996) 575-599. [Abstract] [PDF 235K]
• M. Golubitsky, J.-M. Mao and M. Nicol. Symmetries of periodic solutions for planar potential systems. Proc. Amer. Math. Soc. 124 (1996) 3219-3228. [Abstract] [PDF 267K]
• M. Dellnitz, M. Field, M. Golubitsky, A. Hohmann and J. Ma. Cycling Chaos. Intern. J. Bifur. & Chaos. 5 (4) (1995) 1243-1247. [Abstract] [PDF 246K]
• M. Dellnitz, M. Golubitsky, A. Hohmann and I. Stewart. Spirals in scalar reaction diffusion equations. Intern. J. Bifur. & Chaos. 5 (6) (1995) 1487-1501. [Abstract] [PDF 1.4M]
• B. Dionne, M. Golubitsky, M. Silber and I. Stewart. Time-periodic spatially-periodic planforms in Euclidean equivariant systems. Phil. Trans. R. Soc. London A. 352 (1995) 125-168. [Abstract] [PDF 6.8M]
• M. Field and M. Golubitsky. Symmetric chaos: how and why. Notices AMS. 42 (2) (1995) 240-244. [Abstract] [PDF 116K]
• M. Golubitsky, J. Marsden, I. Stewart and M. Dellnitz. The constrained Liapunov-Schmidt procedure and periodic orbits. Fields Institute Proceedings. 4 (1995) 81-127. [Abstract] [PDF 2.2M]
• M. Golubitsky and M. Nicol. Symmetry detectives for SBR attractors. Nonlinearity. 8 (1995) 1027-1037. [Abstract] [PDF 510K]
• M. Dellnitz, M. Golubitsky and M. Nicol. Symmetry of attractors and the Karhunen-Loeve decomposition. In: Trends and Perspectives in Applied Mathematics. (L. Sirovich, ed.) Appl. Math. Sci. 100 Springer-Verlag, New York, 1994, 73-108. [Abstract] [PDF 1.9M]
• M. Field, M. Golubitsky and M. Nicol. A note on symmetries of invariant sets with compact group actions. In: Equadiff 8. Tatra Mountains Math. Publ. 4 , 1994, 93-104. [Abstract] [PDF 5.3M]
• M. Golubitsky, I. Stewart and B. Dionne. Coupled cells: wreath products and direct products. In: Dynamics, Bifurcation and Symmetry. (P. Chossat, ed.) NATO ARW Series, Kluwer, Amsterdam, 1994, 127-138. [Abstract] [PDF 108K]
• E. Barany, M. Dellnitz and M. Golubitsky. Detecting the symmetry of attractors. Physica D. 67 (1993) 66-87. [Abstract] [PDF 1.3M]
• I.R. Epstein and M. Golubitsky. Symmetric patterns in linear arrays of coupled cells. Chaos. 3 (1) (1993) 1-5. [Abstract] [PDF 332K]
• M. Field and M. Golubitsky. Symmetries on the edge of chaos. New Scientist. 1855 (January 9 1993) 32-35. [Abstract] [PDF 735K]
• M. Golubitsky and I. Stewart. An algebraic criterion for symmetric Hopf bifurcation. Proc. R. Soc. London. 440 (1993) 727-732. [Abstract] [PDF 646K]
• I. Melbourne, M. Dellnitz and M. Golubitsky. The structure of symmetric attractors. Arch. Rational Mech. Anal. 123 (1993) 75-98. [Abstract] [PDF 1.4M]
• E. Allgower, K. Bohmer and M. Golubitsky. Bifurcation and Symmetry. ISNM 104 Birkhauser, Basal, 1992,
• E. Barany, M. Golubitsky and J. Turski. Bifurcations with local gauge symmetries in the Ginzburg-Landau equations. Physica D. 56 (1992) 36-56. [Abstract] [PDF 1.3M]
• M. Dellnitz, M. Golubitsky and I. Melbourne. Mechanisms of symmetry creation. In: Bifurcation and Symmetry. (E. Allgower, K. Boehmer and M. Golubitsky, eds.) ISNM 104 Birkhausser, Basel, 1992, 99-109. [Abstract] [PDF 489K]
• B. Dionne and M. Golubitsky. Planforms in two and three dimensions. ZAMP. 43 (1992) 36-62. [Abstract] [PDF 1.6M]
• W.W. Farr and M. Golubitsky. Rotating chemical waves in the Gray-Scott model. SIAM J. Appl. Math. 52 (1) (1992) 181-221. [Abstract] [PDF 5.1M]
• M. Field and M. Golubitsky. Symmetry in Chaos: A Search for Pattern in Mathematics, Art, and Nature. Oxford University Press, Oxford, 1992, (Translated into: German and French)
• I. Stewart and M. Golubitsky. Fearful Symmetry: Is God a Geometer?. Blackwell Publishers, Oxford, 1992, (Translated into: German, Dutch, Italian, Spanish, Japanese, Greek and Hebrew)
• D.G. Aronson, M. Golubitsky and M. Krupa. Large arrays of Josephson junctions and iterates of maps with S_n symmetry. Nonlinearity. 4 (1991) 861-902. [Abstract] [PDF 2.0M]
• D.G. Aronson, M. Golubitsky and J. Mallet-Paret. Ponies on a merry-go-round in large arrays of Josephson junctions. Nonlinearity. 4 (1991) 903-910. [Abstract] [PDF 365K]
• J.D. Crawford, M. Golubitsky, M.G.M. Gomes, E. Knobloch and I.N. Stewart. Boundary conditions as symmetry constraints. In: Singularity Theory and Its Applications, Warwick 1989, Part II. (M. Roberts and I.N. Stewart, eds.) Lecture Notes in Math. 1463 Springer-Verlag, Heidelberg, 1991, 63-79. [Abstract] [PDF 584K]
• M. Field, M. Golubitsky and I.N. Stewart. Bifurcations on hemispheres. J. Nonlinear Science. 1 (1991) 201-223. [Abstract] [PDF 1.5M]
• M. Golubitsky. Genericity, bifurcation and symmetry. In: Patterns and Dynamics in Reactive Media. (H.L. Swinney, R. Aris and D.G. Aronson, eds.) IMA Volumes in Mathematics and its Applications 37 Springer-Verlag, New York, 1991, 71-88. [Abstract] [PDF 818K]
• M. Golubitsky, M. Krupa and C. Lim. Time-reversibility and particle sedimentation. SIAM J. Appl. Math. 51 (1) (1991) 49-72. [Abstract] [PDF 1.8M]
• M. Field and M. Golubitsky. Symmetric chaos. Computers in Physics. (Sep/Oct 1990) 470-479. [Abstract] [PDF 2.3M]
• S.A. van Gils and M. Golubitsky. A torus bifurcation theorem in the presence of symmetry. Dyn. Diff. Eqn. 2 (2) (1990) 133-163. [Abstract] [PDF 1.2M]
• Li Kaitai, J. Marsden, M. Golubitsky and G. Iooss. Bifurcation Theory and Its Numerical Analysis. Xi'an Jiaotong University Press, Xi'an China, 1989,
• I. Melbourne, P. Chossat and M. Golubitsky. Heteroclinic cycles involving periodic solutions in mode interactions with O(2) symmetry. Proc. Roy. Soc. Edinburgh. 113A (1989) 315-345. [Abstract] [PDF 1.4M]
• A. Vanderbauwhede, M. Krupa and M. Golubitsky. Secondary bifurcations in symmetric systems. In: Differential Equations,. (C.M. Dafermos, G. Ladas and G. Papanicolaou, eds.) Lect. Notes Pure Appl. Math. 118 Marcel Dekker, Inc., New York, 1989, 709-716. [PDF 324K]
• P. Chossat and M. Golubitsky. Symmetry increasing bifurcation of chaotic attractors. Physica D. 32 (1988) 423-436. [PDF 4.1M]
• P. Chossat and M. Golubitsky. Iterates of maps with symmetry. SIAM J. Math. Anal. 19 (6) (1988) 1259-1270. [Abstract] [PDF 1.5M]
• J.D. Crawford, M. Golubitsky and W.F. Langford. Modulated rotating waves in O(2) mode interactions. Dyn. Stab. Sys. 3 No. 3-4 (1988) 159-175. [Abstract] [PDF 762K]
• M. Golubitsky and W.F. Langford. Pattern formation and bistability in flow between counterrotating cylinders. Physica D. 32 (1988) 362-392. [Abstract] [PDF 3.6M]
• M. Golubitsky, I.N. Stewart and D.G. Schaeffer. Singularities and Groups in Bifurcation Theory: Vol. II. Applied Mathematical Sciences; Springer-Verlag. 69 (1988) [PDF 42.0M]
• W.F. Langford, R. Tagg, E. Kostelich, H.L. Swinney and M. Golubitsky. Primary instability and bicriticality in flow between counterrotating cylinders. Phys. Fluids. 31 (4) (1988) 776-785. [Abstract] [PDF 1.7M]
• P. Chossat and M. Golubitsky. Hopf bifurcation in the presence of symmetry, center manifold and Liapunov-Schmidt reduction. In: Oscillation, Bifurcation and Chaos. (F.V. Atkinson, W.F. Langford and A.B. Mingarelli, eds.) CMS-AMS Conf. Proc. Ser. 8 AMS, Providence, 1987, 343-352. [Abstract] [PDF 506K]
• M. Golubitsky and M. Roberts. Degenerate Hopf bifurcation with O(2) symmetry. J. Diff. Eqn. 69 (1987) 216-264. [PDF 1.9M]
• M. Golubitsky and I.N. Stewart. Generic bifurcation of Hamiltonian systems with symmetry. Physica D. 24 (1987) 391-405. [Abstract] [PDF 997K]
• P. Chossat, M. Golubitsky and B.L. Keyfitz. Hopf-Hopf mode interactions with O(2) symmetry. Dyn. Stab. Sys. 1 (4) (1986) 255-292. [Abstract] [PDF 4.4M]
• M. Golubitsky and J. Guckenheimer. Multiparameter Bifurcation Theory. Contemporary Mathematics 56 AMS, 1986,
• M. Golubitsky and I.N. Stewart. Hopf bifurcation with dihedral group symmetry: coupled nonlinear oscillators. In: Multiparameter Bifurcation Theory. (M. Golubitsky and J. Guckenheimer, eds.) Contemporary Mathematics 56 AMS, 1986, 131-173. [Abstract] [PDF 1.8M]
• M. Golubitsky and I.N. Stewart. Symmetry and stability in Taylor-Couette flow. SIAM J. Math. Anal. 17 (2) (1986) 249-288. [Abstract] [PDF 4.4M]
• B.L. Keyfitz, M. Golubitsky, M. Gorman and P. Chossat. The use of symmetry and bifurcation techniques in studying flame stability. In: Reacting Flows: Combustion and Chemical Reactors. (G.S.S. Ludford, ed.) Lectures in Appl. Math. 24, Part 2 AMS, Providence, 1986, 293-315. [Abstract] [PDF 1.0M]
• M. Golubitsky and D.G. Schaeffer. Singularities and Groups in Bifurcation Theory: Vol. I. Applied Mathematical Sciences, Springer-Verlag. 51 (1985) [PDF 44.8M]
• M. Golubitsky and I.N. Stewart. Hopf bifurcation in the presence of symmetry. Arch. Rational Mech. Anal. 87 (2) (1985) 107-165. [Abstract] [PDF 2.5M]
• M. Golubitsky, J. Marsden and D. Schaeffer. Bifurcation problems with hidden symmetries. In: Partial Differential Equations and Dynamical Systems. (W.E. Fitzgibbon III, ed.) Res. Notes in Math. 101 Pitman Press, 1984, 181-210. [PDF 1.0M]
• M. Golubitsky and I.N. Stewart. Hopf bifurcation in the presence of symmetry. Bull. AMS. 11 (2) (1984) 339-342. [Abstract] [PDF 383K]
• M. Golubitsky, J.W. Swift and E. Knobloch. Symmetries and pattern selection in Rayleigh-Benard convection. Physica. 10D (1984) 249-276. [Abstract] [PDF 1.7M]
• E. Ihrig and M. Golubitsky. Pattern selection with O(3) symmetry. Physica. 13D (1984) 1-33. [Abstract] [PDF 2.1M]
• E. Buzano and M. Golubitsky. Bifurcation involving the hexagonal lattice and the planar Benard problem. Phil. Trans. Roy. Soc. London. A308 (1983) 617-667. [PDF 5.5M]
• E. Buzano and M. Golubitsky. Bifurcation involving the hexagonal lattice. Proc. Symp. Pure Math. 40 (1983) 203-210. [PDF 489K]
• M. Golubitsky. The Benard problem, symmetry and the lattice of isotropy subgroups. In: Bifurcation Theory, Mechanics and Physics. (C.P. Bruter et al, eds.) D. Reidel Publishing Co., 1983, 225-256. [Abstract] [PDF 1.5M]
• M. Golubitsky and J. Marsden. The Morse lemma in infinite dimensions via singularity theory. SIAM J. Math. Anal. 14 (1983) 1037-1044. [Abstract] [PDF 908K]
• M. Golubitsky and D. Schaeffer. A discussion of symmetry and symmetry breaking. In: Singularity Theory. (P. Orlik, ed.) Proc. Symp. Pure Math. 40 , 1983, 499-516. [Abstract] [PDF 1.1M]
• M. Golubitsky and D. Schaeffer. Bifurcation with O(3) symmetry including applications to the Benard problem. Commun. Pure & Appl. Math. 35 (1982) 81-111. [PDF 1.2M]
• M. Golubitsky, B.L. Keyfitz and D. Schaeffer. A singularity theory analysis of the thermal chainbranching model. Commun. Pure & Appl. Math. 34 (1981) 433-463. [PDF 7.6M]
• M. Golubitsky and W.F. Langford. Classification and unfoldings of degenerate Hopf bifurcation. J. Diff. Eqns. 41 (1981) 375-415. [Abstract] [PDF 1.7M]
• M. Golubitsky and H.L. Smith. A remark on periodically perturbed bifurcation. In: Differential Equations and Applications to Ecology, Epidemics and Population Problems. Academic Press, 1981, 259-277. [PDF 511K]
• D. Schaeffer and M. Golubitsky. Bifurcation analysis near a double eigenvalue of a model chemical reaction. Arch. Rational Mech. & Anal. 75 (1981) 315-347. [Abstract] [PDF 1.2M]
• M. Golubitsky and B.L. Keyfitz. A qualitative study of the steady-state solutions for a continuous flow stirred tank chemical reactor. SIAM J. Math. Anal. 11 (1980) 316-339. [Abstract] [PDF 1.9M]
• M. Golubitsky and D. Schaeffer. A qualitative approach to steady state bifurcation theory. In: New Approaches to Nonlinear Problems in Dynamics. SIAM, 1980, 43-52, 257-270, 433-436.
• M. Golubitsky and D. Schaeffer. A singularity theory approach to steady state bifurcation theory. In: Nonlinear Partial Differential Equations and Applied Science. Dekker, 1980, 229-254. [PDF 995K]
• M. Golubitsky. A review of Catastrophe Theory and its Applications by Tim Poston and Ian Stewart. Bull. AMS. 1 (3) (1979) 524-532. [PDF 1.1M]
• M. Golubitsky and D. Schaeffer. A theory for imperfect bifurcation via singularity theory. Commun. Pure and Appl. Math. 32 (1979) 1-77. [PDF 4.1M]
• M. Golubitsky and D. Schaeffer. Imperfect bifurcation in the presence of symmetry. Commun. Math. Phys. 67 (1979) 205-232. [PDF 2.6M]
• M. Golubitsky and D. Schaeffer. An analysis of imperfect bifurcation. Annals of New York Acad. of Sci. 316 (1979) 127-133. [PDF 231K]
• D. Schaeffer and M. Golubitsky. Boundary conditions and mode jumping in the buckling of a rectangular plate. Commun. Math. Phys. 69 (1979) 209-236. [Abstract] [PDF 1.4M]
• M. Golubitsky. An introduction to catastrophe theory and its applications. SIAM Review. 20 (2) (1978) 352-387. [PDF 3.8M]
• M. Golubitsky and D. Tischler. A survey on the singularities and stability of differential forms. Asterisque. 59-60 (1978) 43-82. [PDF 1.2M]
• M. Golubitsky and D. Tischler. An example of moduli for singular symplectic forms. Inventiones Math. 38 (1977) 219-225. [Abstract] [PDF 247K]
• M. Golubitsky and D. Tischler. On the non-existence of globally stable forms. Proc. AMS. 58 (1976) 296-300. [Abstract] [PDF 142K]
• M. Golubitsky and D. Tischler. On the local stability of differential forms. Trans. AMS. 223 (1976) 205-221. [Abstract] [PDF 1.3M]
• M. Golubitsky. Contact equivalence for Lagrangian submanifolds. In: Dynamical Systems-Warwick 1974. Lecture Notes Math. 468 Springer Verlag. New York, 1975, 71-73.
• M. Golubitsky and V. Guillemin. Contact equivalence for Lagrangian submanifolds. Adv. Math. 15 (3) (1975) 375-387. [PDF 668K]
• M. Golubitsky, E. Keeler and M. Rothschild. Convergence of the age structure: applications of the projective metric. Theor. Pop. Biol. 7 (1) (1975) 84-93. [Abstract] [PDF 546K]
• M. Golubitsky and D. Schaeffer. Stability of shock waves for a single conservation law. Adv. Math. 16 (1) (1975) 65-71. [PDF 333K]
• M. Golubitsky and V. Guillemin. Stable Mappings and Their Singularities. Graduate Texts in Mathematics; Springer-Verlag. 14 (1973) [PDF 24.9M]
• M. Golubitsky. Primitive actions and maximal subgroups of Lie groups. J. Diff. Geom. 7 (1972) 175-191. [PDF 1.5M]
• M. Golubitsky and B. Rothschild. Primitive subalgebras of exceptional Lie algebras. Pac. J. Math. 39 (2) (1971) 371-393. [Abstract] [PDF 2.1M]
• M. Golubitsky and B. Rothschild. Primitive subalgebras of exceptional Lie algebras. Bull. AMS. 77 (6) (1971) 983-986. [Abstract] [PDF 328K]
• H.S. Wilf and M. Golubitsky. A Computer Simulation in the Study of the Communicability of Diseases. Report, Department of Mathematics, University of Pennsylvania. (1966) [Abstract] [PDF 442K]
• W. Duncan, F. Antoneli and M. Golubitsky. Patterns of homeostasis. preprint. In preparation.
• A. Franci, M. Golubitsky, I. Stewart, A. Bizyaeva and N.E. Leonard. Breaking indecision in multi-agent, multi-option dynamics. SIAM J.Appl.Dynam Sys. To appear. [Abstract] [PDF 1.3M]