Bifurcation of Bounded Solutions of Impulsive Differential Equations

dc.contributor.authorChurch, Kevin E. M.
dc.contributor.authorLiu, Xinzhi
dc.date.accessioned2018-04-20T19:56:13Z
dc.date.available2018-04-20T19:56:13Z
dc.date.issued2016-12-30
dc.descriptionElectronic version of an article published as International Journal of Bifurcation and Chaos, Volume 26, No. 14, 2016, 1-20 doi:10.1142/S0218127416502424 © copyright World Scientific Publishing Company, http://dx.doi.org/10.1142/S0218127416502424en
dc.description.abstractIn this article, we examine nonautonomous bifurcation patterns in nonlinear systems of impulsive differential equations. The approach is based on Lyapunov–Schmidt reduction applied to the linearization of a particular nonlinear integral operator whose zeroes coincide with bounded solutions of the impulsive differential equation in question. This leads to sufficient conditions for the presence of fold, transcritical and pitchfork bifurcations. Additionally, we provide a computable necessary condition for bifurcation in nonlinear scalar impulsive differential equations. Several examples are provided illustrating the results.en
dc.identifier.urihttp://dx.doi.org/10.1142/S0218127416502424
dc.identifier.urihttp://hdl.handle.net/10012/13151
dc.language.isoenen
dc.publisherWorld Scientific Publishingen
dc.subjectImpulsive differential equationsen
dc.subjectbifurcationen
dc.subjectbounded solutionen
dc.subjecthyperbolicityen
dc.subjectexponential dichotomyen
dc.titleBifurcation of Bounded Solutions of Impulsive Differential Equationsen
dc.typeArticleen
dcterms.bibliographicCitationChurch, K. E. M., & Liu, X. (2016). Bifurcation of Bounded Solutions of Impulsive Differential Equations. International Journal of Bifurcation and Chaos, 26(14), 1650242. https://doi.org/10.1142/S0218127416502424en
uws.contributor.affiliation1Faculty of Mathematicsen
uws.contributor.affiliation2Applied Mathematicsen
uws.peerReviewStatusRevieweden
uws.scholarLevelGraduateen
uws.typeOfResourceTexten
uws.typeOfResourceTexten

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