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...

Full description

Bibliographic Details
Main Authors: Reit Marco, Berens Michael, Mathis Wolfgang
Format: Article
Language:English
Published: Polish Academy of Sciences 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
Description
Summary: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.
ISSN:2300-2506