Periodic Canard Trajectories with Multiple Segments Following the Unstable Part of Critical Manifold

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dc.contributor.ISNI0000 0003 5341 0057 (Rachinskii, DI)
dc.contributor.authorKrasnosel'skii, Alexander M.en_US
dc.contributor.authorO'Grady, Edwarden_US
dc.contributor.authorPokrovskii, Alexei V.en_US
dc.contributor.authorRachinskii, Dmitry I.en_US
dc.contributor.utdAuthorRachinskii, Dmitry I.en_US
dc.date.accessioned2014-07-23T19:14:55Z
dc.date.available2014-07-23T19:14:55Z
dc.date.created2012-11-01en_US
dc.date.issued2012-11-01en_US
dc.date.submitted2011-10-01en_US
dc.description.abstractWe consider a scalar fast differential equation which is periodically driven by a slowly varying input. Assuming that the equation depends on n scalar parameters, we present simple sufficient conditions for the existence of a periodic canard solution, which, within a period, makes n fast transitions between the stable branch and the unstable branch of the folded critical curve. The closed trace of the canard solution on the plane of the slow input variable and the fast phase variable has n portions elongated along the unstable branch of the critical curve. We show that the length of these portions and the length of the time intervals of the slow motion separated by the short time intervals of fast transitions between the branches are controlled by the parameters.en_US
dc.identifier.bibliographicCitationKrasnosel'skii, Alexander M., Edward O'Grady, Alexei V. Pokrovskii, and Dmitrii I. Rachinskii. 2013. "Periodic Canard Trajectories with Multiple Segments Following the Unstable Part of Critical Manifold." Discrete and Continuous Dynamical Systems-Series B 18(2): 467-482.en_US
dc.identifier.issn1531-3492en_US
dc.identifier.issue2en_US
dc.identifier.startpage467en_US
dc.identifier.urihttp://hdl.handle.net/10735.1/3787
dc.identifier.volume18en_US
dc.relation.urihttp://dx.doi.org/10.3934/dcdsb.2013.18.467
dc.rights©2013 American Institute of Mathematical Sciencesen_US
dc.sourceDiscrete and Continuous Dynamical Systems-Series B
dc.subjectPeriodic solutionen_US
dc.subjectCanard trajectoryen_US
dc.subjectTopological degreeen_US
dc.subjectDegree theoryen_US
dc.subjectStabilityen_US
dc.titlePeriodic Canard Trajectories with Multiple Segments Following the Unstable Part of Critical Manifolden_US
dc.typeTexten_US
dc.type.genreArticleen_US

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