An analytical method for computing Hopf bifurcation curves in neural field networks with space-dependent delays

Romain Veltz 1, 2, 3
2 IMAGINE [Marne-la-Vallée]
CSTB - Centre Scientifique et Technique du Bâtiment, LIGM - Laboratoire d'Informatique Gaspard-Monge, ENPC - École des Ponts ParisTech
3 NEUROMATHCOMP - Mathematical and Computational Neuroscience
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR6621
Abstract : We give an analytical parametrization of the curves of purely imaginary eigenvalues in the delay-parameter plane of the linearized neural field network equations with space-dependent delays. In order to determine if the rightmost eigenvalue is purely imaginary, we have to compute a finite number of such curves; the number of curves is bounded by a constant for which we give an expression. The Hopf bifurcation curve lies on these curves.
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Journal articles
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https://hal.inria.fr/hal-00845727
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Submitted on : Wednesday, July 17, 2013 - 4:12:28 PM
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Romain Veltz. An analytical method for computing Hopf bifurcation curves in neural field networks with space-dependent delays. Comptes Rendus Mathématique, Elsevier Masson, 2011, 349 (13-14), pp.749--752. ⟨10.1016/j.crma.2011.06.014⟩. ⟨hal-00845727⟩

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