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dc.contributor.authorRicard, M.R.
dc.contributor.authorMischler, Stéphane
dc.date.accessioned2014-02-13T13:03:20Z
dc.date.available2014-02-13T13:03:20Z
dc.date.issued2009
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/12659
dc.language.isoenen
dc.subjectHopf bifurcationen
dc.subjectTuring instabilitiesen
dc.subjectReaction-diffusionen
dc.subjectAveragingen
dc.subject.ddc519en
dc.titleTuring Instabilities at Hopf Bifurcationen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenTuring–Hopf instabilities for reaction-diffusion systems provide spatially inhomogeneous time-periodic patterns of chemical concentrations. In this paper we suggest a way for deriving asymptotic expansions to the limit cycle solutions due to a Hopf bifurcation in two-dimensional reaction systems and we use them to build convenient normal modes for the analysis of Turing instabilities of the limit cycle. They extend the Fourier modes for the steady state in the classical Turing approach, as they include time-periodic fluctuations induced by the limit cycle. Diffusive instabilities can be properly considered because of the non-catastrophic loss of stability that the steady state shows while the limit cycle appears. Moreover, we shall see that instabilities may appear even though the diffusion coefficients are equal. The obtained normal modes suggest that there are two possible ways, one weak and the other strong, in which the limit cycle generates oscillatory Turing instabilities near a Turing–Hopf bifurcation point. In the first case slight oscillations superpose over a dominant steady inhomogeneous pattern. In the second, the unstable modes show an intermittent switching between complementary spatial patterns, producing the effect known as twinkling patterns.en
dc.relation.isversionofjnlnameJournal of Nonlinear Science
dc.relation.isversionofjnlvol19en
dc.relation.isversionofjnlissue5en
dc.relation.isversionofjnldate2009
dc.relation.isversionofjnlpages467-496en
dc.relation.isversionofdoihttp://dx.doi.org/10.1007/s00332-009-9041-6en
dc.relation.isversionofjnlpublisherSpringeren
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen


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