Nonsmooth bifurcations in a piecewise-linear model of the Colpitts oscillator

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dc.contributor.authorMaggio, Gian Mario
dc.contributor.authorDi Bernardo, Mario
dc.contributor.authorKennedy, Michael Peter
dc.contributor.funderEuropean Commissionen
dc.contributor.funderForbairten
dc.contributor.funderNuffield Foundation, United Kingdomen
dc.date.accessioned2010-04-28T12:53:26Z
dc.date.available2010-04-28T12:53:26Z
dc.date.issued2000-08
dc.date.updated2010-04-27T15:41:53Z
dc.description.abstractThis paper deals with the implications of considering a first-order approximation of the circuit nonlinearities in circuit simulation and design. The Colpitts oscillator is taken as a case study and the occurrence of discontinuous bifurcations, namely, border-collision bifurcations, in a piecewise-linear model of the oscillator is discussed. In particular, we explain the mechanism responsible for the dramatic changes of dynamical behavior exhibited by this model when one or more of the circuit parameters are varied. Moreover, it is shown how an approximate one-dimensional (1-D) map for the Colpitts oscillator can be exploited for predicting border-collision bifurcations. It turns out that at a border collision bifurcation, a 1-D return map of the Colpitts oscillator exhibits a square-root-like singularity. Finally, through the 1-D map, a two-parameter bifurcation analysis is carried out and the relationships are pointed out between border-collision bifurcations and the conventional bifurcations occurring in smooth systemsen
dc.description.sponsorshipEuropean Commission (TMR program, Grant ERBFMBICT950310); Forbairt (International Collaboration Grant IC/98/052); Nuffield Foundation, United Kingdom (NUF-NAL scheme and the Institute Project 99-1-02)en
dc.description.statusPeer revieweden
dc.description.versionPublished Versionen
dc.format.mimetypeapplication/pdfen
dc.identifier.citationMaggio, G.M., di Bernardo, M., Kennedy, M.P., 2000. Nonsmooth bifurcations in a piecewise-linear model of the Colpitts oscillator. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 47(8), pp.1160-1177. doi: 10.1109/81.873871en
dc.identifier.doi10.1109/81.873871
dc.identifier.endpage1177en
dc.identifier.issn1057-7122
dc.identifier.issued8en
dc.identifier.journaltitleIEEE Transactions on Circuits and Systems I: Fundamental Theory and Applicationsen
dc.identifier.startpage1160en
dc.identifier.urihttps://hdl.handle.net/10468/169
dc.identifier.volume47en
dc.language.isoenen
dc.publisherIEEEen
dc.rights©2000 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.en
dc.subjectBorder-collision bifurcationsen
dc.subjectColpitts oscillatoren
dc.subjectGrazingen
dc.subjectNonsmooth systemsen
dc.subjectOne-dimensional mapen
dc.subjectSliding modeen
dc.subject.lcshBifurcation theoryen
dc.subject.lcshRadio frequency oscillatorsen
dc.subject.lcshPiecewise linear topologyen
dc.titleNonsmooth bifurcations in a piecewise-linear model of the Colpitts oscillatoren
dc.typeArticle (peer-reviewed)en
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