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Search Results: 1 - 10 of 2338 matches for " Tomasz Kapitaniak "
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Using chaos synchronization to estimate the largest lyapunov exponent of nonsmooth systems
Andrzej Stefanski,Tomasz kapitaniak
Discrete Dynamics in Nature and Society , 2000, DOI: 10.1155/s1026022600000200
Abstract: We describe the method of estimation of the largest Lyapunov exponent of nonsmooth dynamical systems using the properties of chaos synchronization. The method is based on the coupling of two identical dynamical systems and is tested on two examples of Duffing oscillator: (i) with added dry friction, (ii) with impacts.
Synchronous motion of two vertically excited planar elastic pendula
Marcin Kapitaniak,Przemyslaw Perlikowski,Tomasz Kapitaniak
Physics , 2012, DOI: 10.1016/j.cnsns.2012.12.030
Abstract: 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.
Analysis of transition between different ringing schemes of the church bell
Piotr Brzeski,Tomasz Kapitaniak,Przemyslaw Perlikowski
Physics , 2015,
Abstract: In this paper we investigate dynamics of church bells, characterize their most common working regimes and investigate how to obtain them. To simulate the behavior of the yoke-bell-clapper system we use experimentally validated hybrid dynamical model developed basing on the detailed measurements of the biggest bell in the Cathedral Basilica of St Stanislaus Kostka, Lodz, Poland. We introduce two parameters that describes the yoke design and the propulsion mechanism and analyze their influence on the systems' dynamics. We develop two-parameter diagrams that allow to asses conditions that ensures proper and smooth operation of the bell. Similar charts can be calculated for any existing or non-existing bell and used when designing its mounting and propulsion. Moreover, we propose simple and universal launching procedure that allows to decrease the time that is needed to reach given attractor. Presented results are robust and indicate methods to increase the chance that the instrument will operate properly and reliably regardless of changes in working conditions.
Blowout bifurcation of chaotic saddles
Tomasz Kapitaniak,Ying-Cheng Lai,Celso Grebogi
Discrete Dynamics in Nature and Society , 1998, DOI: 10.1155/s1026022699000023
Abstract: Chaotic saddles are nonattracting dynamical invariant sets that can lead to a variety of physical phenomena. We describe the blowout bifurcation of chaotic saddles located in the symmetric invariant manifold of coupled systems and discuss dynamical phenomena associated with this bifurcation.
Synchronization of two self-excited double pendula
Piotr Koluda,Przemyslaw Perlikowski,Krzysztof Czolczynski,Tomasz Kapitaniak
Physics , 2014, DOI: 10.1140/epjst/e2014-02129-7
Abstract: We consider the synchronization of two self-excited double pendula. We show that such pendula hanging on the same beam can have four different synchronous configurations. Our approximate analytical analysis allows us to derive the synchronization conditions and explain the observed types of synchronization. We consider an energy balance in the system and describe how the energy is transferred between the pendula via the oscillating beam, allowing thus the pendula synchronization. Changes and stability ranges of the obtained solutions with increasing and decreasing masses of the pendula are shown using path-following.
The dynamics of co- and counter rotating coupled spherical pendulums
Blazej Witkowski,Przemyslaw Perlikowski,Awadhesh Prasad,Tomasz Kapitaniak
Physics , 2014, DOI: 10.1140/epjst/e2014-02136-8
Abstract: The dynamics of co- and counter-rotating coupled spherical pendulums (two lower pendulums are mounted at the end of the upper pendulum) is considered. Linear mode analysis shows the existence of three rotating modes. Starting from linear modes allow we calculate the nonlinear normal modes, which are and present them in frequency-energy plots. With the increase of energy in one mode we observe a symmetry breaking pitchfork bifurcation. In the second part of the paper we consider energy transfer between pendulums having different energies. The results for co-rotating (all pendulums rotate in the same direction) and counter-rotating motion (one of lower pendulums rotates in the opposite direction) are presented. In general, the energy fluctuations in counter-rotating pendulums are found to be higher than in the co-rotating case.
The dynamics of the pendulum suspended on the forced Duffing oscillator
Piotr Brzeski,Przemyslaw Perlikowski,Serhiy Yanchuk,Tomasz Kapitaniak
Physics , 2012, DOI: 10.1016/j.jsv.2012.07.021
Abstract: We investigate the dynamics of the pendulum suspended on the forced Duffing oscillator. The detailed bifurcation analysis in two parameter space (amplitude and frequency of excitation) which presents both oscillating and rotating periodic solutions of the pendulum has been performed. We identify the areas with low number of coexisting attractors in the parameter space as the coexistence of different attractors has a significant impact on the practical usage of the proposed system as a tuned mass absorber.
Riddling and chaotic synchronization of coupled piecewise-linear Lorenz maps
Marcos C. Verges,Rodrigo Frehse Pereira,Sergio R. Lopes,Ricardo L. Viana,Tomasz Kapitaniak
Physics , 2009, DOI: 10.1016/j.physa.2009.02.015
Abstract: We investigate the parametric evolution of riddled basins related to synchronization of chaos in two coupled piecewise-linear Lorenz maps. Riddling means that the basin of the synchronized attractor is shown to be riddled with holes belonging to another basin in an arbitrarily fine scale, which has serious consequences on the predictability of the final state for such a coupled system. We found that there are wide parameter intervals for which two piecewise-linear Lorenz maps exhibit riddled basins (globally or locally), which indicates that there are riddled basins in coupled Lorenz equations, as previously suggested by numerical experiments. The use of piecewise-linear maps makes it possible to prove rigorously the mathematical requirements for the existence of riddled basins.
Analog to Digital Conversion in Physical Measurements
T. Kapitaniak,K. Zyczkowski,U. Feudel,C. Grebogi
Physics , 1999, DOI: 10.1016/S0960-0779(99)00003-X
Abstract: 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.
Amplitude equations and fast transition to chaos in rings of coupled oscillators
S. Yanchuk,P. Perlikowski,M. Wolfrum,A. Stefanski,T. Kapitaniak
Physics , 2010,
Abstract: We study the coupling induced destabilization in an array of identical oscillators coupled in a ring structure where the number of oscillators in the ring is large. The coupling structure includes different types of interactions with several next neighbors. We derive an amplitude equation of Ginzburg-Landau type, which describes the destabilization of a uniform stationary state in a ring with a large number of nodes. Applying these results to unidirectionally coupled Duffing oscillators, we explain the phenomenon of a fast transition to chaos, which has been numerically observed in such systems. More specifically, the transition to chaos occurs on an interval of a generic control parameter that scales as the inverse square of the size of the ring, i.e. for sufficiently large system, we observe practically an immediate transition to chaos.
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