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:	Andronov-Hopf bifurcation nonlinear amplifier ambiguities
Online Access:	http://www.degruyter.com/view/j/aee.2016.65.issue-2/aee-2016-0025/aee-2016-0025.xml?format=INT

id	doaj-art-4980e588b6d9485b8077c1781f25e57b
recordtype	oai_dc
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

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

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