Spatial Unfolding of Homoclinic Bifurcations

  • P. Coullet
  • E. Risler
  • N. Vanderberghe
Part of the NATO Science Series book series (ASIC, volume 569)


We consider solutions which are homogeneous in space, periodic in time, and close to being homoclinic for a partial differential equation. We show that such solutions are generically unstable with respect to large wavelength perturbations, and that the instability can be of two different types: either the well-known Kuramoto phase insta- bility, or a fundamentally different kind of instability, called self-parametric, displaying a period-doubling and an intrinsic wavelength. We also consider the case where the spatial parity symmetry breaks.


Periodic Solution Local Frame Phase Instability Homoclinic Solution Homoclinic Bifurcation 
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Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • P. Coullet
    • 1
    • 2
  • E. Risler
    • 1
  • N. Vanderberghe
    • 1
  1. 1.INLNValbonneFrance
  2. 2.l’Institut Universitaire de FranceFrance

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