# 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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