arXiv subjects

Tomasz Kapitaniak

Publications and source records attributed to Tomasz Kapitaniak.

26 records · Page 2Linked to original sources

arXiv2016

The smallest chimera states

We demonstrate that chimera behavior can be observed in small networks consisting of three identical oscillators, with mutual all-to-all coupling. Three different types of chimeras, characterized by the coexistence of two coherent oscillators and one incoherent oscillator (i.e. rotating with another frequency) have been identified, where the oscillators show periodic (two types) and chaotic (one type) behaviors. Typical bifurcations at the transitions from full synchronization to chimera states and between different types of chimeras have been described. Parameter regions for the chimera states are obtained in the form of Arnold tongues, issued from a singular parameter point. Our analysis suggests that chimera states can be observed in small networks, relevant to various real-world systems.

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arXiv2016

Perpetual points and periodic perpetual loci in maps

We introduce the concepts of perpetual points and periodic perpetual loci in discrete--time systems (maps). The occurrence and analysis of these points/loci are shown and basic examples are considered. We discuss the potential usage and properties of introduced concepts. The comparison of perpetual points and loci in discrete--time and continuous--time systems is presented. Discussed methods can be widely applied in other dynamical systems.

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arXiv2015

Analysis of transition between different ringing schemes of the church bell

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.

physics.class-ph↗

arXiv2014

The dynamics of co- and counter rotating coupled spherical pendulums

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.

physics.class-ph↗

arXiv2014

Synchronization of two self-excited double pendula

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.

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arXiv2012

The dynamics of the pendulum suspended on the forced Duffing oscillator

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.

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arXiv2012

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.

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arXiv2009

Riddling and chaotic synchronization of coupled piecewise-linear Lorenz maps

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.

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