Essential instabilities of fronts: bifurcation, and bifurcation failure

@article{Sandstede2001EssentialIO,
  title={Essential instabilities of fronts: bifurcation, and bifurcation failure},
  author={Bj{\"o}rn Sandstede and Arnd Scheel},
  journal={Dynamical Systems},
  year={2001},
  volume={16},
  pages={1 - 28}
}
Various instability mechanisms of fronts in reaction-diffusion systems are analysed; the emphasis is on instabilities that have the potential to create modulated (i.e. time-periodic) waves near the primary front. Hopf bifurcations caused by point spectrum with associated localized eigenfunctions provide an example of such an instability. A different kind of instability occurs if one of the asymptotic rest states destabilizes: these instabilities are caused by essential spectrum. It is… 
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