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Discretization analysis of bifurcation based nonlinear amplifiers.
- Source :
-
Advances in Radio Science . 2017, Vol. 15, p43-47. 5p. - Publication Year :
- 2017
-
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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ELECTRONIC amplifiers
*DISCRETIZATION methods
*BIFURCATION theory
Subjects
Details
- Language :
- English
- ISSN :
- 16849965
- Volume :
- 15
- Database :
- Academic Search Index
- Journal :
- Advances in Radio Science
- Publication Type :
- Academic Journal
- Accession number :
- 125428451
- Full Text :
- https://doi.org/10.5194/ars-15-43-2017