Rocky Mountain Journal of Mathematics

The Effect of Delay and Diffusion on Spontaneous Symmetry Breaking in Functional Differential Equations

Jianhong Wu

Full-text: Open access

Article information

Rocky Mountain J. Math., Volume 25, Number 1 (1995), 545-556.

First available in Project Euclid: 5 June 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34K15
Secondary: 92E20: Classical flows, reactions, etc. [See also 80A30, 80A32]


Wu, Jianhong. The Effect of Delay and Diffusion on Spontaneous Symmetry Breaking in Functional Differential Equations. Rocky Mountain J. Math. 25 (1995), no. 1, 545--556. doi:10.1216/rmjm/1181072301.

Export citation


  • J.C. Alexander and G. Auchmuty, Global bifurcations of phase-locked oscillations, Arch. Rational Mech. Anal. 93 (1986), 253-270.
  • S.-N. Chow, J. Mallet-Paret and J. Yorke, Global Hopf bifurcation from a multiple eigenvalue, Nonlinear Anal. 2 (1978), 753-763.
  • K. Geba, W. Krawcewicz and J. Wu, An equivariant degree with applications to symmetric bifurcation problems, III: Hopf bifurcation theorems of functional differential equations with symmetries, preprint.
  • M. Golubitsky and I.N. Stewart, Hopf bifuration with dihedral group symmetry: Coupled nonlinear oscillators, in Multiparameter bifurcation theory (C.M. Golubitsky and J. Guckenheimer, eds.), 1985, 131-173.
  • --------, Hopf bifurcation in the presence of symmetry, Arch. Rational Mech. Anal. 817 (1985), 107-165.
  • M. Golubitsky, I. Stewart and D.G. Schaeffer, Singularities and groups in bifurcation theory, Vol. 2, Springer-Verlag, New York, Berlin, 1988.
  • J.K. Hale, Theory of functional differential equations, Springer-Verlag, New York, Berlin 1977.
  • M.W. Hirsch, The dynamical systems approach to differential equations, Bull. Amer. Math. Soc. 11 (1984), 1-64.
  • W. Krawcewicz and J. Wu, Discrete waves and phase-locked oscillations in the growth of a single-species populations over a patchy environment, Open Systems and Information Dynamics 1 (1992), 127-147.
  • D.H. Sattinger, Spontaneous symmetry breaking in bifurcation problems, in Systems in science (C.B. Gruker and R.S. Millman, eds.), Plenum Press, New York, 1980, 365-383.
  • A. Vanderbauwhede, Local bifuration and symmetries, Research Notes in Math. 75, Pitman, London, 1982.
  • J. Wu, The existence and stability of symmetric periodic solutions in functional differential equations, preprint.