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Wyszukujesz frazę "Chaos" wg kryterium: Temat


Wyświetlanie 1-8 z 8
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:
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:
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 1-8 z 8

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