Spatial Unfolding of Homoclinic Bifurcations

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

Abstract

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.

Keywords

Manifold Argentina 

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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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