Discretization analysis of bifurcation based nonlinear amplifiers

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dc.identifier.uri http://dx.doi.org/10.15488/2094
dc.identifier.uri http://www.repo.uni-hannover.de/handle/123456789/2119
dc.contributor.author Feldkord, Sven
dc.contributor.author Reit, Marco
dc.contributor.author Mathis, Wolfgang
dc.date.accessioned 2017-10-24T08:01:09Z
dc.date.available 2017-10-24T08:01:09Z
dc.date.issued 2017
dc.identifier.citation Feldkord, S.; Reit, M.; Mathis, W.: Discretization analysis of bifurcation based nonlinear amplifiers. In: Advances in Radio Science 15 (2017), S. 43-47. DOI: https://doi.org/10.5194/ars-15-43-2017
dc.description.abstract Recently, for modeling biological amplification processes, nonlinear amplifiers based on the supercritical Andronov-Hopf bifurcation have been widely analyzed analytically. For technical realizations, digital systems have become the most relevant systems in signal processing applications. The underlying continuous-time systems are transferred to the discrete-time domain using numerical integration methods. Within this contribution, effects on the qualitative behavior of the Andronov-Hopf bifurcation based systems concerning numerical integration methods are analyzed. It is shown exemplarily that explicit Runge-Kutta methods transform the truncated normalform equation of the Andronov-Hopf bifurcation into the normalform equation of the Neimark-Sacker bifurcation. Dependent on the order of the integration method, higher order terms are added during this transformation. A rescaled normalform equation of the Neimark-Sacker bifurcation is introduced that allows a parametric design of a discrete-time system which corresponds to the rescaled Andronov-Hopf system. This system approximates the characteristics of the rescaled Hopf-type amplifier for a large range of parameters. The natural frequency and the peak amplitude are preserved for every set of parameters. The Neimark-Sacker bifurcation based systems avoid large computational effort that would be caused by applying higher order integration methods to the continuous-time normalform equations. © Author(s) 2017. eng
dc.language.iso eng
dc.publisher Göttingen : Copernicus GmbH
dc.relation.ispartofseries Advances in Radio Science 15 (2017)
dc.rights CC BY 3.0 Unported
dc.rights.uri https://creativecommons.org/licenses/by/3.0/
dc.subject Amplifiers (electronic) eng
dc.subject Bifurcation (mathematics) eng
dc.subject Continuous time systems eng
dc.subject Digital control systems eng
dc.subject Discrete time control systems eng
dc.subject Integration eng
dc.subject Numerical methods eng
dc.subject Runge Kutta methods eng
dc.subject Signal processing eng
dc.subject Time domain analysis eng
dc.subject Andronov-Hopf bifurcation eng
dc.subject Computational effort eng
dc.subject Discrete - time systems eng
dc.subject Explicit Runge-Kutta methods eng
dc.subject Neimark-Sacker bifurcation eng
dc.subject Numerical integration methods eng
dc.subject Signal processing applications eng
dc.subject Technical realization eng
dc.subject Hopf bifurcation eng
dc.subject.ddc 621,3 | Elektrotechnik, Elektronik ger
dc.title Discretization analysis of bifurcation based nonlinear amplifiers
dc.type article
dc.type Text
dc.relation.issn 1684-9965
dc.relation.doi https://doi.org/10.5194/ars-15-43-2017
dc.bibliographicCitation.volume 15
dc.bibliographicCitation.firstPage 43
dc.bibliographicCitation.lastPage 47
dc.description.version publishedVersion
tib.accessRights frei zug�nglich

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