Marty Golubitsky

Reprint List

Department of Mathematics
651 Philip G. Hoffman Hall
University of Houston
Houston, TX 77204-3008

E-MAIL: dynamics@math.uh.edu
PHONE: 713-743-3490
FAX: 713-743-3505

Hopf bifurcation

• 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 421K]

• 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 268K]

• 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.C.A. Leite and M. Golubitsky. Homogeneous three-cell networks. Nonlinearity. 19 (2006) 2313-2363. [Abstract] [PDF 497K]

• 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]

• M. Golubitsky, M. Nicol and I. Stewart. Some curious phenomena in coupled cell systems. J. Nonlinear Sci. 14 (2) (2004) 207-236. [Abstract] [PDF 1.6M]

• 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 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, 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, I. Stewart, P.L. Buono and J.J. Collins. A modular network for legged locomotion. Physica D. 115 (1998) 56-72. [Abstract]

• 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. Dellnitz, M. Golubitsky, A. Hohmann and I. Stewart. Spirals in scalar reaction diffusion equations. Intern. J. Bifur. & Chaos. 5 (6) (1995) 1487-1501. [Abstract]

• 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]

• M. Golubitsky and I. Stewart. An algebraic criterion for symmetric Hopf bifurcation. Proc. R. Soc. London. 440 (1993) 727-732. [Abstract] [PDF 646K]

• W.W. Farr and M. Golubitsky. Rotating chemical waves in the Gray-Scott model. SIAM J. Appl. Math. 52 (1) (1992) 181-221. [Abstract]

• 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]

• M. Golubitsky and W.F. Langford. Pattern formation and bistability in flow between counterrotating cylinders. Physica D. 32 (1988) 362-392. [Abstract]

• M. Golubitsky, I.N. Stewart and D.G. Schaeffer. Singularities and Groups in Bifurcation Theory: Vol. II. Applied Mathematical Sciences 69 Springer-Verlag, New York, 1988,

• 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]

• M. Golubitsky and M. Roberts. Degenerate Hopf bifurcation with O(2) symmetry. J. Diff. Eqn. 69 (1987) 216-264.

• 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]

• 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]

• M. Golubitsky and I.N. Stewart. Symmetry and stability in Taylor-Couette flow. SIAM J. Math. Anal. 17 (2) (1986) 249-288. [Abstract]

• M. Golubitsky and D.G. Schaeffer. Singularities and Groups in Bifurcation Theory: Vol. I. Applied Mathematical Sciences 51 Springer-Verlag, New York, 1985,

• 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 and I.N. Stewart. Hopf bifurcation in the presence of symmetry. Bull. AMS. 11 (2) (1984) 339-342. [Abstract] [PDF 383K]

• M. Golubitsky and W.F. Langford. Classification and unfoldings of degenerate Hopf bifurcation. J. Diff. Eqns. 41 (1981) 375-415. [Abstract]

• 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 To appear. [Abstract] [PDF 633K]