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dc.contributor.authorKudryashova, Elena V.
dc.date.accessioned2009-09-16T13:01:48Z
dc.date.available2009-09-16T13:01:48Z
dc.date.issued2009
dc.identifier.isbn978-951-39-3666-2
dc.identifier.otheroai:jykdok.linneanet.fi:1110753
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/21762
dc.description.abstractThe present work is devoted to calculation of periodic solutions and bifurcation research in quadratic systems, Lienard system, and non-unimodal one-dimensional discrete maps using modern computational capabilities and symbolic computing packages.In the first chapter the problem of Academician A.N. Kolmogorov on localization and modeling of cycles of quadratic systems is considered. For the investigation of small limit cycles (so-called local 16th Hilbert’s problem) the method of calculation of Lyapunov quantities (or Poincaré-Lyapunov constants) is used. To calculate symbolic expressions for the Lyapunov quantities the Lyapunov method to the case of non-analytical systems was generalized. Following the works of L.A. Cherkas and G.A. Leonov, the symbolic algorithms for transformation of quadratic systems to special Lienard systems were developed. For the first time general symbolic expressions of first four Lyapunov quantities for Lienard systems are obtained. The large limit cycles (or "normal" limit cycles) for quadratic and Lienard systems with parameters corresponding to the domain of existence of a large cycle, obtained by G.A. Leonov, are presented. Visualization on the plane of parameters of a Lienard system of the domain of parameters of quadratic systems with four limit cycles, obtained by S.L. Shi, is realized.The second chapter of the thesis is devoted to non-unimodal one-dimensional discrete maps describing operation of digital phase locked loop (PLL). Qualitative analysis of PLL equations helps one to determine necessary system operating conditions (which, for example, include phase synchronization and clock-skew elimination). In this work, application of the qualitative theory of dynamical systems, special analytical methods, and modern mathematical packages has helped us to advance considerably in calculation of bifurcation values and to define numerically fourteen bifurcation values of the DPLL’s parameter. It is shown that for the obtained bifurcation values of a non-unimodal map, the effect of convergence similar to Feigenbaum’s effect is observeden
dc.description.abstractElena Kudryashovan väitöstutkimuksessa selvitettiin matemaattisten mallien ratkeavuutta käyttäen nykyaikaisia laskentamahdollisuuksia ja symbolisen laskennan ohjelmistoja. Tutkimuksen käytännön sovellutukset liittyvät tietokoneiden toiminnan tehostamiseen.fi
dc.format.extent79 sivua
dc.language.isoeng
dc.publisherUniversity of Jyväskylä
dc.relation.ispartofseriesJyväskylä studies in computing
dc.relation.isversionofISBN 978-951-39-3633-4, 978-951-39-3533-4 virh.
dc.subject.othersymbolinen laskenta
dc.subject.otherdynaamiset järjestelmät
dc.subject.otherdynamical systems
dc.subject.otherlimit cycles
dc.subject.otherphase locked loops
dc.subject.otherPLL
dc.subject.otherbifurcation
dc.subject.otherKolmogorov's problem
dc.subject.otherLyapunov quantities
dc.subject.otherLienard system
dc.titleCycles in continuous and discrete dynamical systems : computations, computer-assisted proofs, and computer experiments
dc.typeDiss.fi
dc.identifier.urnURN:ISBN:978-951-39-3666-2
dc.type.dcmitypeTexten
dc.type.ontasotVäitöskirjafi
dc.type.ontasotDoctoral dissertationen
dc.contributor.tiedekuntaInformaatioteknologian tiedekuntafi
dc.contributor.tiedekuntaFaculty of Information Technologyen
dc.contributor.yliopistoUniversity of Jyväskyläen
dc.contributor.yliopistoJyväskylän yliopistofi
dc.contributor.oppiaineTietotekniikkafi
dc.relation.issn1456-5390
dc.relation.numberinseries107
dc.rights.accesslevelopenAccessfi
dc.subject.ysotietojenkäsittely
dc.subject.ysomatemaattiset mallit
dc.subject.ysomallintaminen


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