207 research outputs found
Analog to Digital Conversion in Physical Measurements
There exist measuring devices where an analog input is converted into a
digital output. Such converters can have a nonlinear internal dynamics. We show
how measurements with such converting devices can be understood using concepts
from symbolic dynamics. Our approach is based on a nonlinear one-to-one mapping
between the analog input and the digital output of the device. We analyze the
Bernoulli shift and the tent map which are realized in specific analog/digital
converters. Furthermore, we discuss the sources of errors that are inevitable
in physical realizations of such systems and suggest methods for error
reduction.Comment: 9 pages in LATEX, 4 figures in ps.; submitted to 'Chaos, Solitons &
Fractals
Basin stability approach for quantifying responses of multistable systems with parameters mismatch
Acknowledgement This work is funded by the National Science Center Poland based on the decision number DEC-2015/16/T/ST8/00516. PB is supported by the Foundation for Polish Science (FNP).Peer reviewedPublisher PD
Controlling multistability in coupled systems with soft impacts
This work has been supported by Lodz University of Technology own Scholarship Fund (PB) and by Stipend for Young Outstanding Scientists from Ministry of Science and Higher Education of Poland (PP). PB is supported by the Foundation for Polish Science (FNP).Peer reviewedPostprin
1991] âAnalytic predictors for strange nonâchaotic attractors,â Phys
Analytic conditions are used to predict the bounds in parameter space of the regions of existence of a non-chaotic strange attractor for the quasi-periodically forced van der Pol equation. One bound arises from the condition for existence of a simple quasi-periodic response to the forcing; the other appears to be related to the occurrence of a Hopf bifurcation in the averaged form of the equation
Practical Stability of Chaotic Attractors
Abstract--In this paper we introduce the concept of practical stability and practical stability in finite time for chaotic attractors. The connection between practical and asymptotic stability is discussed
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Sample-based approach can outperform the classical dynamical analysis - Experimental confirmation of the basin stability method
In this paper we show the first broad experimental confirmation of the basin stability approach. The basin stability is one of the sample-based approach methods for analysis of the complex, multidimensional dynamical systems. We show that investigated method is a reliable tool for the analysis of dynamical systems and we prove that it has a significant advantages which make it appropriate for many applications in which classical analysis methods are difficult to apply. We study theoretically and experimentally the dynamics of a forced double pendulum. We examine the ranges of stability for nine different solutions of the system in a two parameter space, namely the amplitude and the frequency of excitation. We apply the path-following and the extended basin stability methods (Brzeski et al., Meccanica 51(11), 2016) and we verify obtained theoretical results in experimental investigations. Comparison of the presented results show that the sample-based approach offers comparable precision to the classical method of analysis. However, it is much simpler to apply and can be used despite the type of dynamical system and its dimensions. Moreover, the sample-based approach has some unique advantages and can be applied without the precise knowledge of parameter values
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Erratum: Sample-based approach can outperform the classical dynamical analysis - experimental confirmation of the basin stability method
The original version of this Article contained a typographical error in the spelling of the author T. Kapitaniak, which was incorrectly given as T. Kapitaniakenglish. This has now been corrected in the PDF and HTML versions of the Article
Stabilization of unstable steady states by variable delay feedback control
We report on a dramatic improvement of the performance of the classical
time-delayed autosynchronization method (TDAS) to control unstable steady
states, by applying a time-varying delay in the TDAS control scheme in a form
of a deterministic or stochastic delay-modulation in a fixed interval around a
nominal value . The successfulness of this variable delay feedback control
(VDFC) is illustrated by a numerical control simulation of the Lorenz and
R\"{o}ssler systems using three different types of time-delay modulations: a
sawtooth wave, a sine wave, and a uniform random distribution. We perform a
comparative analysis between the VDFC method and the standard TDAS method for a
sawtooth-wave modulation by analytically determining the domains of control for
the generic case of an unstable fixed point of focus type.Comment: 7 pages, 4 figures, RevTe
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