Hopf Bifurcation and Exchange of Stability in Diffusive Media

@article{Brand2004HopfBA,
  title={Hopf Bifurcation and Exchange of Stability in Diffusive Media},
  author={Thomas Brand and Markus Kunze and Guido Schneider and Thorsten Seelbach},
  journal={Archive for Rational Mechanics and Analysis},
  year={2004},
  volume={171},
  pages={263-296}
}
Abstract.We consider solutions bifurcating from a spatially homogeneous equilibrium under the assumption that the associated linearization possesses a continuous spectrum up to the imaginary axis, for all values of the bifurcation parameter, and that a pair of imaginary eigenvalues crosses the imaginary axis. For a reaction-diffusion-convection system we investigate the nonlinear stability of the trivial solution with respect to spatially localized perturbations, prove the occurrence of a Hopf… 
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