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

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dc.contributor.author Maggio, Gian Mario
dc.contributor.author Di Bernardo, Mario
dc.contributor.author Kennedy, Michael Peter
dc.date.accessioned 2010-04-28T12:53:26Z
dc.date.available 2010-04-28T12:53:26Z
dc.date.issued 2000-08
dc.identifier.citation Maggio, 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: 10.1109/81.873871 en
dc.identifier.volume 47 en
dc.identifier.issued 8 en
dc.identifier.startpage 1160 en
dc.identifier.endpage 1177 en
dc.identifier.issn 1057-7122
dc.identifier.uri http://hdl.handle.net/10468/169
dc.identifier.doi 10.1109/81.873871
dc.description.abstract This 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 systems en
dc.description.sponsorship European 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.format.mimetype application/pdf en
dc.language.iso en en
dc.publisher IEEE en
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.subject Border-collision bifurcations en
dc.subject Colpitts oscillator en
dc.subject Grazing en
dc.subject Nonsmooth systems en
dc.subject One-dimensional map en
dc.subject Sliding mode en
dc.subject.lcsh Bifurcation theory en
dc.subject.lcsh Radio frequency oscillators en
dc.subject.lcsh Piecewise linear topology en
dc.title Nonsmooth bifurcations in a piecewise-linear model of the Colpitts oscillator en
dc.type Article (peer-reviewed) en
dc.internal.authorcontactother Michael Peter Kennedy, Vice President Research, University College Cork, Cork, Ireland. +353-21-490-3000 Email: peter.kennedy@ucc.ie en
dc.internal.availability Full text available en
dc.date.updated 2010-04-27T15:41:53Z
dc.description.version Published Version en
dc.internal.rssid 347354
dc.contributor.funder European Commission en
dc.contributor.funder Forbairt en
dc.contributor.funder Nuffield Foundation, United Kingdom en
dc.description.status Peer reviewed en
dc.identifier.journaltitle IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications en
dc.internal.IRISemailaddress peter.kennedy@ucc.ie en


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