54 research outputs found
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
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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
Synchronous motion of two vertically excited planar elastic pendula
The dynamics of two planar elastic pendula mounted on the horizontally
excited platform have been studied. We give evidence that the pendula can
exhibit synchronous oscillatory and rotation motion and show that stable
in-phase and anti-phase synchronous states always co-exist. The complete
bifurcational scenario leading from synchronous to asynchronous motion is
shown. We argue that our results are robust as they exist in the wide range of
the system parameters.Comment: Submitte
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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
Dynamical response of a rocking rigid block
This is the author accepted manuscript. The final version is available from AIP Publishing via the DOI in this recordData accessibility: The data that support the findings of this study are available from the corresponding author upon reasonable request.This paper investigates the complex dynamical behavior of a rigid block structure under
harmonic ground excitation, thereby mimicking, for instance, the oscillation of the system under seismic excitation or containers placed on a ship under periodic acting of sea
waves. The equations of motion are derived assuming a large frictional coefficient at the
interface between the block and the ground, in such a way that sliding cannot occur. In
addition, the mathematical model assumes a loss of kinetic energy when an impact with
the ground takes place. The resulting mathematical model is then formulated and studied in the framework of impulsive dynamical systems. Its complex dynamical response
is studied in detail using two different approaches, based on direct numerical integration
and path-following techniques, the latter implemented via the continuation platform COCO
(Dankowicz & Schilder). Our study reveals the presence of various dynamical phenomena,
such as branching points, fold and period-doubling bifurcation of limit cycles, symmetric
and asymmetric periodic responses, as well as chaotic motion. By using basin stability
method we also investigate the properties of solutions and their ranges of existence in
phase and parameters spaces. Moreover, the study considers ground excitation conditions
leading to the overturning of the block structure and shows parameters regions wherein
such behavior can be avoidedEngineering and Physical Sciences Research Council (EPSRC)National Science Centre, Polan
DelayAndPeriodicity
Systems with time delay play an important role in modeling of many physical
and biological processes. In this paper we describe generic properties of
systems with time delay, which are related to the appearance and stability of
periodic solutions. In particular, we show that delay systems generically have
families of periodic solutions, which are reappearing for infinitely many delay
times. As delay increases, the solution families overlap leading to increasing
coexistence of multiple stable as well as unstable solutions. We also consider
stability issue of periodic solutions with large delay by explaining asymptotic
properties of the spectrum of characteristic multipliers. We show that the
spectrum of multipliers can be splitted into two parts: pseudo-continuous and
strongly unstable. The pseudo-continuous part of the spectrum mediates
destabilization of periodic solutions.Comment: 24 pages, 9 figure
Periodic patterns in a ring of delay-coupled oscillators.
We describe the appearance and stability of spatiotemporal periodic patterns (rotating waves) in unidirectional rings of coupled oscillators with delayed couplings. We show how delays in the coupling lead to the splitting of each rotating wave into several new ones. The appearance of rotating waves is mediated by the Hopf bifurcations of the symmetric equilibrium. We also conclude that the coupling delays can be effectively replaced by increasing the number of oscillators in the chain. The phenomena are shown for the Stuart-Landau oscillators as well as for the coupled FitzHugh-Nagumo systems modeling an ensemble of spiking neurons interacting via excitatory chemical synapses
<Contributed Talk 9>HOW CHAOTIC (OR RANDOM) IS THE DICE THROW?
[Date] November 28 (Mon) - December 2 (Fri), 2011: [Place] Kyoto University Clock Tower Centennial Hall, Kyoto, JAPA
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