Hopf Bifurcation and Exchange of Stability in Diffusive Media |
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Authors: | Thomas Brand Markus Kunze Guido Schneider Thorsten Seelbach |
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Institution: | (1) Mathematisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany;(2) FB6 – Mathematik, Universität Essen, D-45117 Essen, Germany;(3) Mathematisches Institut I, Universität Karlsruhe, D-76128 Karlsruhe, Germany |
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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 bifurcation and the nonlinear stability of the bifurcating time-periodic solutions, again with respect to spatially localized perturbations. |
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