Artykuły (WM)

Stały URI dla kolekcjihttp://hdl.handle.net/11652/206

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2004 - 200912010 - 20148

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Autorsearch.filters.applied.operator.equals: search.filters.author.Kapitaniak, Tomasz

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Teraz wyświetlane 1 - 9 z 9
  • Pozycja
    Optimization of the Control System Parameters with Use of the New Simple Method of the Largest Lyapunov Exponent Estimation.
    (Lodz University of Technology. Faculty of Mechanical Engineering. Department Division of Dynamics., 2013) Balcerzak, Marek; Dąbrowski, Artur; Kapitaniak, Tomasz; Jach, Anna
    This text covers application of Largest Lapunov Exponent (LLE) as a criterion for control performance assessment (CPA) in a simulated control system. The main task is to find a simple and effective method to search for the best configuration of a controller in a control system. In this context, CPA criterion based on calculation of LLE by means of a new method [3] is compared to classical CPA criteria used in control engineering [1]. Introduction contains references to previous publications on Lyapunov stability. Later on, description of classical criteria for CPA along with formulae is presented. Significance of LLE in control systems is explained. Moreover, new efficient formula for calculation of LLE [3] is shown. In the second part simulation of the control system used for experiment is described. The next part contains results of the simulation in which typical criteria for CPA are compared with criterion based on value of LLE. In the last part results of the experiment are summed up and conclusions are drawn.
  • Pozycja
    Lag Synchronization in Coupled Multistable van der Pol-Duffing Oscillators
    (2014) Dudkowski, Dawid; Kuźma, Patrycja; Kapitaniak, Tomasz
    We consider the system of externally excited identical van der Pol-Duffing oscillators unidirectionally coupled in a ring. When the coupling is introduced, each of the oscillator’s trajectories is on different attractor. We study the changes in the dynamics due to the increase in the coupling coefficient. Studying the phase of the oscillators, we calculate the parameter value for which we obtain the antiphase lag synchronization of the system and also the bifurcation values for which we observe qualitative changes in the dynamics of already synchronized system. We give evidence that lag synchronization is typical for coupled multistable systems.
  • Pozycja
    Different types of chimera states: An interplay between spatial and dynamical chaos
    (2014) Dudkowski, Dawid; Maistrenko, Yuri; Kapitaniak, Tomasz
    We discuss the occurrence of chimera states in networks of nonlocally coupled bistable oscillators, in which individual subsystems are characterized by the coexistence of regular (a fixed point or a limit cycle) and chaotic attractors. By analyzing the dependence of the network dynamics on the range and strength of coupling, we identify parameter regions for various chimera states, which are characterized by different types of chaotic behavior at the incoherent interval. Besides previously observed chimeras with space-temporal and spatial chaos in the incoherent intervals we observe another type of chimera state in which the incoherent interval is characterized by a central interval with standard space-temporal chaos and two narrow side intervals with spatial chaos. Our findings for the maps as well as for time-continuous van der Pol–Duffing’s oscillators reveal that this type of chimera states represents characteristic spatiotemporal patterns at the transition from coherence to incoherence.
  • Pozycja
    Coupling multistable systems: uncertainty due to the initial positions on the attractors
    (2014) Kuźma, Patrycja; Kapitaniak, Marcin; Kapitaniak, Tomasz
    We consider the coupling of multistable nonidentical systems. For small values of the coupling coefficient the behavior of the coupled system strongly depends on the actual position of trajectories on their attractors in the moment when the coupling is introduced. After reaching the coupling threshold value, this dependence disappears. We give an evidence that this behavior is robust as it exists for a wide range of parameters and different types of coupling. We argue why this behavior cannot be considered as a dependence on the initial conditions.
  • Pozycja
    Bifurcations of Oscillatory and Rotational Solutions of Double Pendulum with Parametric Vertical Excitation
    (Hindawi Publishing Corporation, 2014-06) Marszal, Michał; Jankowski, Krzysztof; Perlikowski, Przemysław; Kapitaniak, Tomasz; Division of Dynamics. Faculty of Mechanical Engineering. Lodz University of Technology.; Katedra Dynamiki Maszyn. Wydział Mechaniczny. Politechnika Łódzka.
    This paper investigates dynamics of double pendulum subjected to vertical parametric kinematic excitation. It includes detailed bifurcation diagrams in two-parameter space (excitation’s frequency and amplitude) for both oscillations and rotations in the domain of periodic solutions.
  • Pozycja
    Energy method for position stability analysis of critical points of robot manipulators.
    (Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej, 2004) Szumiński, Przemysław; Kapitaniak, Tomasz; Stefański, Andrzej
    An energy method for the position stability analysis of critical points (equilibrium positions) of dynamical systems with an arbitrary finite number of degrees of freedom is presented. The method proposed consists in the analysis of the potential energy balance of a perturbation of an arbitrary number of generalised co-ordinates of the dynamical system in order to establish the energy stability of individual degrees of freedom and of the whole system. In the case of mechanical systems, the position stability criterion, understood as minimisation of loads of driving systems with conservative forces, is discussed. Some examples of application of the method to the position stability analysis of critical points of one- and two-degree-of-freedom systems are analysed.
  • Pozycja
    Application of artificial neural networks in parametrical investigations of the energy flow and synchronization.
    (Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej, 2010) Dąbrowski, Artur; Jach, Anna; Kapitaniak, Tomasz
    Dynamics of nonlinear systems is a very complicated problem with many aspects to be recognized. Numerous methods are used to investigate such systems. Their careful analysis is connected with long-time simulations. Thus, there is great need for methods that would simplify these processes. In the paper, an application of Artificial Neural Networks (ANNs) supporting the recognition of the energy flow and the synchronization with use of Impact Maps is introduced. This connection applies an idea of the Energy Vector Space in the system with impacts. An energy flow direction change with the synchronization as a transitional state is shown. A new type of the index allowing one to control the system dynamic state is introduced. Results of the numerical simulations are used in the neural network teaching process. Results of a comparison of the straight impact map simulation and the neural network prediction are shown. Prediction of system parameters for the energy flow synchronization state with use of the neural network is presented.
  • Pozycja
    Energy balance of two synchronized self-excited pendulums with different masses.
    (Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej, 2012) Kapitaniak, Tomasz; Czołczyński, Krzysztof; Perlikowski, Przemysław; Stefański, Andrzej
    We consider the synchronization of two self-excited pendulums with different masses. We show that such pendulums hanging on the same beam can show almost-complete (in-phase) and almost-antiphase synchronizations in which the difference of the pendulums displacements is small. Our approximate analytical analysis allows one to derive the synchronization conditions and explains the observed types of synchronizations as well as gives an approximate formula for amplitudes of both the pendulums and the phase shift between them. We consider the energy balance in the system and show how the energy is transferred between the pendulums via the oscillating beam allowing synchronization of the pendulums.
  • Pozycja
    Coupling multistable systems: uncertainly due to the initial positions on the attractors.
    (Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej, 2014) Kuźma, Patrycja; Kapitaniak, Marcin; Kapitaniak, Tomasz
    We consider the coupling of multistable nonidentical systems. For small values of the coupling coefficient the behavior of the coupled system strongly depends on the actual position of trajectories on their attractors in the moment when the coupling is introduced. After reaching the coupling threshold value, this dependence disappears. We give an evidence that this behavior is robust as it exists for a wide range of parameters and different types of coupling. We argue why this behavior cannot be considered as a dependence on the initial conditions.