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    Wyświetlanie 1-11 z 11
    Tytuł:
    Different synchronization schemes for chaotic Rikitake systems
    Autorzy:
    Ali Khan, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/265096.pdf
    Data publikacji:
    2013
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    kontrola chaosu
    chaos
    system Rikitake
    chaotic system
    chaos synchronization
    chaos control
    Rikitake system
    Opis:
    This paper presents the chaos synchronization by designing a different type of controllers. Firstly, we propose the synchronization of bi-directional coupled chaotic Rikitake systems via hybrid feedback control. Secondly, we study the synchronization of unidirectionally coupled Rikitake systems using hybrid feedback control. Lastly, we investigate the synchronization of unidirectionally coupled Rikitake chaotic systems using tracking control. Comparing all the results, finally, we conclude that tracking control is more effective than feedback control. Simulation results are presented to show the efficiency of synchronization schemes.
    Źródło:
    International Journal of Applied Mechanics and Engineering; 2013, 18, 2; 383-393
    1734-4492
    2353-9003
    Pojawia się w:
    International Journal of Applied Mechanics and Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Attainability analysis in the problem of stochastic equilibria synthesis for nonlinear discrete systems
    Autorzy:
    Bashkirtseva, I.
    Ryashko, L.
    Powiązania:
    https://bibliotekanauki.pl/articles/330694.pdf
    Data publikacji:
    2013
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    stochastic sensitivity function
    attainability
    chaos suppression
    Opis:
    A nonlinear discrete-time control system forced by stochastic disturbances is considered. We study the problem of synthesis of the regulator which stabilizes an equilibrium of the deterministic system and provides required scattering of random states near this equilibrium for the corresponding stochastic system. Our approach is based on the stochastic sensitivity functions technique. The necessary and important part of the examined control problem is an analysis of attainability. For 2D systems, a detailed investigation of attainability domains is given. A parametrical description of the attainability domains for various types of control inputs in a stochastic Henon model is presented. Application of this technique for suppression of noise-induced chaos is demonstrated.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2013, 23, 1; 5-16
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Numerical studies of nonlinear gearing models using bond graph method
    Autorzy:
    Margielewicz, J.
    Wojnarowski, J.
    Zawiślak, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/264969.pdf
    Data publikacji:
    2018
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    chaos
    wibracje nieliniowe
    wykładnik Lapunowa
    rozwidlenia
    nonlinear vibrations
    Lapunov exponent
    bifurcations
    Opis:
    The present paper is dedicated to computer simulations performed using a numerical model of a one-stage gear. The motion equations were derived utilizing the bond graph method. The formulated model takes into consideration the variable stiffness of toothings as well as an inter-tooth clearance which has been represented via discontinuous elements with so called dead zones. As a result of these assumptions, the nonlinear model was obtained which enables representation of the dynamic phenomena of the considered gear. In the paper, an influence of errors of gear wheels’ co-operation on the character of excited dynamic phenomena was studied. The methodology of the analyses consists in utilization of the following tools: color maps of distribution of the maximal Lapunov coefficient and bifurcation diagrams. Based upon them, the parameters were determined, for which the Poincare portrait represents a structure of the chaotic attractor. For the identified attractors, the initial attractors were calculated numerically - which along with the changes of the control parameters are subjected to multiplication, stretching or rotation.
    Źródło:
    International Journal of Applied Mechanics and Engineering; 2018, 23, 4; 885-896
    1734-4492
    2353-9003
    Pojawia się w:
    International Journal of Applied Mechanics and Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A dynamic bi-orthogonal field equation approach to efficient Bayesian inversion
    Autorzy:
    Tagade, P. M.
    Choi, H. L.
    Powiązania:
    https://bibliotekanauki.pl/articles/330516.pdf
    Data publikacji:
    2017
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    Bayesian framework
    stochastic partial differential equation
    Karhunen–Loève expansion
    generalized polynomial chaos
    dynamically biorthogonal field equations
    ramy Bayesa
    stochastyczne równanie różniczkowe
    przekształcenie Karhunena-Loeve'a
    chaos wielomianowy
    Opis:
    This paper proposes a novel computationally efficient stochastic spectral projection based approach to Bayesian inversion of a computer simulator with high dimensional parametric and model structure uncertainty. The proposed method is based on the decomposition of the solution into its mean and a random field using a generic Karhunen–Loève expansion. The random field is represented as a convolution of separable Hilbert spaces in stochastic and spatial dimensions that are spectrally represented using respective orthogonal bases. In particular, the present paper investigates generalized polynomial chaos bases for the stochastic dimension and eigenfunction bases for the spatial dimension. Dynamic orthogonality is used to derive closed-form equations for the time evolution of mean, spatial and the stochastic fields. The resultant system of equations consists of a partial differential equation (PDE) that defines the dynamic evolution of the mean, a set of PDEs to define the time evolution of eigenfunction bases, while a set of ordinary differential equations (ODEs) define dynamics of the stochastic field. This system of dynamic evolution equations efficiently propagates the prior parametric uncertainty to the system response. The resulting bi-orthogonal expansion of the system response is used to reformulate the Bayesian inference for efficient exploration of the posterior distribution. The efficacy of the proposed method is investigated for calibration of a 2D transient diffusion simulator with an uncertain source location and diffusivity. The computational efficiency of the method is demonstrated against a Monte Carlo method and a generalized polynomial chaos approach.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2017, 27, 2; 229-243
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Synchronization of an uncertain Duffing oscillator with higher order chaotic systems
    Autorzy:
    Kabziński, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/330344.pdf
    Data publikacji:
    2018
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    chaos synchronization
    adaptive control
    Duffing oscillator
    synchronizacja chaosu
    sterowanie adaptacyjne
    oscylator Duffinga
    Opis:
    The problem of practical synchronization of an uncertain Duffing oscillator with a higher order chaotic system is considered. Adaptive control techniques are used to obtain chaos synchronization in the presence of unknown parameters and bounded, unstructured, external disturbances. The features of the proposed controllers are compared by solving Duffing–Arneodo and Duffing–Chua synchronization problems.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2018, 28, 4; 625-634
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The dynamics of a parametrically driven damped pendulum
    Autorzy:
    Das, A.
    Kumar, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/265555.pdf
    Data publikacji:
    2015
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    parametric vibration
    Floquet analysis
    Lyapunov exponents
    stroboscopic maps
    chaos
    teoria Floqueta
    funkcja Lapunowa
    Opis:
    Ordered and chaotic states of a parametrically driven planar pendulum with viscous damping are numerically investigated. The damping makes the number of chaotic windows fewer but with larger width. Stroboscopic maps of the chaotic motion of the pendulum, driven either subharmonically or harmonically, show strange attractors with inversion symmetry in the phase plane.
    Źródło:
    International Journal of Applied Mechanics and Engineering; 2015, 20, 2; 257-266
    1734-4492
    2353-9003
    Pojawia się w:
    International Journal of Applied Mechanics and Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Image cipher applications using the elliptical curve and chaos
    Autorzy:
    Silva-García, Víctor Manuel
    Flores-Carapia, Rolando
    Rentería-Márquez, Carlos
    Luna-Benoso, Bejamín
    Chimal-Eguía, Juan Carlos
    Powiązania:
    https://bibliotekanauki.pl/articles/329867.pdf
    Data publikacji:
    2020
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    elliptic curve
    chaos
    discrete Fourier transform
    image ciphering
    krzywa eliptyczna
    dyskretna transformata Fouriera
    Opis:
    A novel symmetric cryptosystem of the substitution permutation network type is presented for image encryption in 14 rounds. An algorithm is developed to generate 15 keys to encrypt images where each key is the image size. These keys are calculated using an elliptic curve with a constant zero value. The proposed curve is non-singular, non-supersingular, nor trace one. Chaos is employed to find a generating element in a cyclic subgroup and it is produced using the logistic map equation. In addition, a 16 × 16 substitution box is constructed using both chaos and an algorithm that defines a bijective function. The following tools are used in order to measure the degree of randomness of the encrypted figures: entropy, correlation, the discrete Fourier transform and a goodness-of-fit test with the chi-square distribution. Furthermore, an image size variable permutation is applied in the first round, and its inverse in the fourteenth.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2020, 30, 2; 377-391
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Ergodic theory approach to chaos: remarks and computational aspects
    Autorzy:
    Mitkowski, P. J.
    Mitkowski, W.
    Powiązania:
    https://bibliotekanauki.pl/articles/331446.pdf
    Data publikacji:
    2012
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    twierdzenie ergodyczne
    chaos
    miara niezmiennicza
    ergodic theory
    invariant measures
    attractors
    delay differential equations
    Opis:
    We discuss basic notions of the ergodic theory approach to chaos. Based on simple examples we show some characteristic features of ergodic and mixing behaviour. Then we investigate an infinite dimensional model (delay differential equation) of erythropoiesis (red blood cell production process) formulated by Lasota. We show its computational analysis on the previously presented theory and examples. Our calculations suggest that the infinite dimensional model considered possesses an attractor of a nonsimple structure, supporting an invariant mixing measure. This observation verifies Lasota's conjecture concerning nontrivial ergodic properties of the model.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2012, 22, 2; 259-267
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Spike patterns and chaos in a map-based neuron model
    Autorzy:
    Bartłomiejczyk, Piotr
    Llovera Trujillo
    Signerska-Rynkowska, Justyna
    Powiązania:
    https://bibliotekanauki.pl/articles/24200689.pdf
    Data publikacji:
    2023
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    neuronal dynamics
    β-transformations
    Farey–Lorenz permutations
    periodic spiking
    chaos
    dynamika neuronalna
    permutacje Fareya-Lorenza
    Opis:
    The work studies the well-known map-based model of neuronal dynamics introduced in 2007 by Courbage, Nekorkin and Vdovin, important due to various medical applications. We also review and extend some of the existing results concerning β-transformations and (expanding) Lorenz mappings. Then we apply them for deducing important properties of spike-trains generated by the CNV model and explain their implications for neuron behaviour. In particular, using recent theorems of rotation theory for Lorenz-like maps, we provide a classification of periodic spiking patterns in this model.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2023, 33, 3; 395--408
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Simple environment for developing methods of controlling chaos in spatially distributed systems
    Autorzy:
    Korus, Ł.
    Powiązania:
    https://bibliotekanauki.pl/articles/907826.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    stabilność układu
    wykładnik Lapunowa
    metoda Lyapunova
    coupled map lattice
    spatiotemporal chaos
    system stability
    Lyapunov exponents
    net direction phase
    Opis:
    The paper presents a simple mathematical model called a coupled map lattice (CML). For some range of its parameters, this model generates complex, spatiotemporal behavior which seems to be chaotic. The main purpose of the paper is to provide results of stability analysis and compare them with those obtained from numerical simulation. The indirect Lyapunov method and Lyapunov exponents are used to examine the dependence on initial conditions. The net direction phase is introduced to measure the symmetry of the system state trajectory. In addition, a real system, which can be modeled by the CML, is presented. In general, this article describes basic elements of environment, which can be used for creating and examining methods of chaos controlling in systems with spatiotemporal dynamics.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2011, 21, 1; 149-159
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Efficiency analysis of control algorithms in spatially distributed systems with chaotic behavior
    Autorzy:
    Korus, Ł.
    Powiązania:
    https://bibliotekanauki.pl/articles/331175.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    controlling spatiotemporal chaos
    coupled map lattice
    system stability
    Lyapunov exponent
    net direction phase
    stabilność układu
    wykładnik Lapunowa
    kierunek fazy
    Opis:
    The paper presents results of examination of control algorithms for the purpose of controlling chaos in spatially distributed systems like the coupled map lattice (CML). The mathematical definition of the CML, stability analysis as well as some basic results of numerical simulation exposing complex, spatiotemporal and chaotic behavior of the CML were already presented in another paper. The main purpose of this article is to compare the efficiency of controlling chaos by simple classical algorithms in spatially distributed systems like CMLs. This comparison is made based on qualitative and quantitative evaluation methods proposed in the previous paper such as the indirect Lyapunov method, Lyapunov exponents and the net direction phase indicator. As a summary of this paper, some conclusions which can be useful for creating a more efficient algorithm of controlling chaos in spatially distributed systems are made.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2014, 24, 4; 759-770
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-11 z 11

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