Ambiguities in input-output behavior of driven nonlinear systems close to bifurcation

Since the so-called Hopf-type amplifier has become an established element in the modeling of the mammalian hearing organ, it also gets attention in the design of nonlinear amplifiers for technical applications. Due to its pure sinusoidal response to a sinusoidal input signal, the amplifier based on...

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Main Authors: Reit Marco, Berens Michael, Mathis Wolfgang
Format: Article
Language:English
Published: Sciendo 2016-06-01
Series:Archives of Electrical Engineering
Subjects:
Online Access:http://www.degruyter.com/view/j/aee.2016.65.issue-2/aee-2016-0025/aee-2016-0025.xml?format=INT
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spelling doaj-art-4980e588b6d9485b8077c1781f25e57b2018-09-02T08:15:27ZengSciendoArchives of Electrical Engineering2300-25062016-06-0165233734710.1515/aee-2016-0025aee-2016-0025Ambiguities in input-output behavior of driven nonlinear systems close to bifurcationReit Marco0Berens Michael1Mathis Wolfgang2Leibniz Universität Hannover Institute of Theoretical Electrical Engineering Appelstraße 9A, 30167 Hannover, GermanyLeibniz Universität Hannover Institute of Theoretical Electrical Engineering Appelstraße 9A, 30167 Hannover, GermanyLeibniz Universität Hannover Institute of Theoretical Electrical Engineering Appelstraße 9A, 30167 Hannover, GermanySince the so-called Hopf-type amplifier has become an established element in the modeling of the mammalian hearing organ, it also gets attention in the design of nonlinear amplifiers for technical applications. Due to its pure sinusoidal response to a sinusoidal input signal, the amplifier based on the normal form of the Andronov-Hopf bifurcation is a peculiar exception of nonlinear amplifiers. This feature allows an exact mathematical formulation of the input-output characteristic and thus deeper insights of the nonlinear behavior. Aside from the Hopf-type amplifier we investigate an extension of the Hopf system with focus on ambiguities, especially the separation of solution sets, and double hysteresis behavior in the input-output characteristic. Our results are validated by a DSP implementation.http://www.degruyter.com/view/j/aee.2016.65.issue-2/aee-2016-0025/aee-2016-0025.xml?format=INTAndronov-Hopfbifurcationnonlinear amplifierambiguities
institution Open Data Bank
collection Open Access Journals
building Directory of Open Access Journals
language English
format Article
author Reit Marco
Berens Michael
Mathis Wolfgang
spellingShingle Reit Marco
Berens Michael
Mathis Wolfgang
Ambiguities in input-output behavior of driven nonlinear systems close to bifurcation
Archives of Electrical Engineering
Andronov-Hopf
bifurcation
nonlinear amplifier
ambiguities
author_facet Reit Marco
Berens Michael
Mathis Wolfgang
author_sort Reit Marco
title Ambiguities in input-output behavior of driven nonlinear systems close to bifurcation
title_short Ambiguities in input-output behavior of driven nonlinear systems close to bifurcation
title_full Ambiguities in input-output behavior of driven nonlinear systems close to bifurcation
title_fullStr Ambiguities in input-output behavior of driven nonlinear systems close to bifurcation
title_full_unstemmed Ambiguities in input-output behavior of driven nonlinear systems close to bifurcation
title_sort ambiguities in input-output behavior of driven nonlinear systems close to bifurcation
publisher Sciendo
series Archives of Electrical Engineering
issn 2300-2506
publishDate 2016-06-01
description Since the so-called Hopf-type amplifier has become an established element in the modeling of the mammalian hearing organ, it also gets attention in the design of nonlinear amplifiers for technical applications. Due to its pure sinusoidal response to a sinusoidal input signal, the amplifier based on the normal form of the Andronov-Hopf bifurcation is a peculiar exception of nonlinear amplifiers. This feature allows an exact mathematical formulation of the input-output characteristic and thus deeper insights of the nonlinear behavior. Aside from the Hopf-type amplifier we investigate an extension of the Hopf system with focus on ambiguities, especially the separation of solution sets, and double hysteresis behavior in the input-output characteristic. Our results are validated by a DSP implementation.
topic Andronov-Hopf
bifurcation
nonlinear amplifier
ambiguities
url http://www.degruyter.com/view/j/aee.2016.65.issue-2/aee-2016-0025/aee-2016-0025.xml?format=INT
_version_ 1612652468985921536