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References
Alexander, J. C., Bifurcation of zeroes of parametrized functions, J. Func. Anal. 29 (1978), 37–53.
Alexander, J. C., & J. F. G. Auchmuty, Global branching of waves, Manus. Math. 27 (1979), 159–166.
Alexander, J. C., & P. M. Fitzpatrick, The homotopy of certain spaces of non-linear operators, and its relation to global bifurcation of the fixed points of parametrized condensing operators, J. Func. Anal. 34 (1979), 87–106.
Alexander, J. C., & J. Yorke, Global bifurcation of periodic orbits, Am J. Math. 100 (1978), 263–292.
Auchmuty, J. F. G., Bifurcating waves, Bifurcation Theory and Applications in Scientific Disciplines, O. Gurel & O. E. Rossler, ed., Ann. N.Y. Acad. Sci. 316 (1979), 263–278.
Auchmuty, J. F. G., Bifurcation analysis of reaction-diffusion equations V. Rotating waves on a disc, in Partial Differential equations and Dynamical Systems, W. E. Fitz-Gibbon, ed., Pitman Research Notes in Math. 101 (1984), 35–63.
Chandra, J., & A. L. Scott, (eds), Coupled Nonlinear Oscillators, North Holland Math. Studies 80 (1983).
Chow, S. N., & J. M. Mallet-Paret, The Fuller index and global Hopf bifurcation, J. Diff. Eq. 29 (1978), 66–85.
DeKleine, H. A., E. Kennedy & N. MacDonald, A Study of coupled chemical oscillators, preprint (1982).
Fitzpatrick, P. M., Linearization, bifurcation and homotopy, to be published.
Howard, L. N., Nonlinear oscillations in Oscillations in Biology, F. R. Hoppen-Steadt, ed., A.M.S. Lectures in Applied Mathematics 17 (1979), 1–69.
Kopell, N., Forced and coupled oscillators in biological applications, Proc. Int. Cong. of Mathematicians, Warsaw (1983) (to appear).
Othmer, H. G., & L. E. Scriven, Instability and dynamic pattern in cellular networks, J. Theor. Biol. 32 (1971), 507.
Nicolis, G., & I. Prigogine, Self-organization in Nonequilibrium Systems, Wiley-Interscience, New York (1977).
Nussbaum, R., A Hopf global bifurcation theorem for retarded functional differential equations, Trans. Am. Math. Soc., 238 (1978), 139–164.
Ruelle, D., Bifurcations in the Presence of a Symmetry Group, Arch. Rational Mech. Anal. 51 (1973) pp. 136–152.
Schecter, S., Bifurcations with Symmetry, Section 8 of “The Hopf Bifurcation and its Applications” ed. Marsden & McCracken, Springer Verlag, N.Y. (1976) pp. 224–249.
Smale, S., A mathematical model of two cells via Turing's equation in Some Mathematical Questions in Biology V, J. D. Cowan, ed., A.M.S. Lectures on Mathematics in the Life Sciences 6 (1974), 15–26.
Turing, A. M., The chemical basis of morphogenesis, Phil. Trans. Roy. Soc. London B237 (1952), 37–72.
Winfree, A. T., The Geometry of Biological Time, Springer-Verlag, Berlin Heidelberg New York (1980).
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Communicated by M. Golubitsky
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Alexander, J.C., Auchmuty, G. Global bifurcations of phase-locked oscillators. Arch. Rational Mech. Anal. 93, 253–270 (1986). https://doi.org/10.1007/BF00281500
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DOI: https://doi.org/10.1007/BF00281500