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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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 |
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author |
Reit Marco Berens Michael Mathis Wolfgang |
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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 |