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    Wyświetlanie 1-8 z 8
    Tytuł:
    Some theorems of Rabinowitz type for nonlinearizable eigenvalue problems
    Autorzy:
    Przybycin, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/2049049.pdf
    Data publikacji:
    2004
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    nonlinear eigenvalue problem
    bifurcation point
    bifurcation interval
    Opis:
    We discuss the structure of the solution set for nonlinearizable eigenvalue problems in a Hilbert space.
    Źródło:
    Opuscula Mathematica; 2004, 24, 1; 115-121
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Numerical detection of bifurcation point in the curve
    Autorzy:
    Gulgowski, Jacek
    Powiązania:
    https://bibliotekanauki.pl/articles/748467.pdf
    Data publikacji:
    2015
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    path following algorithm
    bifurcation point
    bifurcation simplex
    Opis:
    We are presenting a numerical method which detects the presence and position of a  bifurcation simplex, the regular $(k+1)$-dimensional simplex, which may be considered as "fat bifurcation point", in the curve of zeroes of the $C^1$ map $f:{\mathbb R}^{k+1}\to{\mathbb R}^k$. On the other hand the bifurcation simplex appears in the neighbourhood of the bifurcation point, meaning that we have the method to locate the bifurcation point as well. The method does not require any estimation of the derivative of the function $f$ and refers to the values of the map $f$ only in the vertices of certain triangulation. The bifurcation simplex is detected by change of the Brouwer degree value of the restriction of the map $f$ to the appropriate $k$-simplex.This publication is co-financed by the European Union as part of the European Social Fund within the project Center for Applications of Mathematics.
    Źródło:
    Mathematica Applicanda; 2015, 43, 1
    1730-2668
    2299-4009
    Pojawia się w:
    Mathematica Applicanda
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Nonlinear eigenvalue problems for fourth order ordinary differential equations
    Autorzy:
    Przybycin, Jolanta
    Powiązania:
    https://bibliotekanauki.pl/articles/1311640.pdf
    Data publikacji:
    1995
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    bifurcation point
    bifurcation interval
    Leray-Schauder degree
    characteristic value
    Opis:
    This paper was inspired by the works of Chiappinelli ([3]) and Schmitt and Smith ([7]). We study the problem ℒu = λau + f(·,u,u',u'',u''') with separated boundary conditions on [0,π], where ℒ is a composition of two operators of Sturm-Liouville type. We assume that the nonlinear perturbation f satisfies the inequality |f(x,u,u',u'',u''')| ≤ M|u|. Because of the presence of f the considered equation does not in general have a linearization about 0. For this reason the global bifurcation theorem of Rabinowitz ([5], [6]) is not applicable here. We use the properties of Leray-Schauder degree to establish the existence of nontrivial solutions and describe their location. The results obtained are similar to those proved by Chiappinelli for Sturm-Liouville operators.
    Źródło:
    Annales Polonici Mathematici; 1994-1995, 60, 3; 249-253
    0066-2216
    Pojawia się w:
    Annales Polonici Mathematici
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Behaviour of Solutions to Marchuks Model Depending on a Time Delay
    Autorzy:
    Bodnar, M.
    Foryś, U.
    Powiązania:
    https://bibliotekanauki.pl/articles/929743.pdf
    Data publikacji:
    2000
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    antygen
    przeciwciało
    opóźnienie różniczkowe
    antigen
    antibody
    plasma cell
    organ-target
    delay differential equation
    stationary state
    stability
    bifurcation point
    Opis:
    Marchuk's model of an immune reaction is a system of differential equations with a time delay. The aim of this paper is to study the behaviour of solutions to Marchuk's model depending upon the delay of immune reaction and the history of an illness. We study Marchuk's model without delays, with aconstant delay and with an infinite delay. A continuous dependence on thedelay is considered. Bifurcation points are found using computer simulations.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2000, 10, 1; 97-112
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Comparison of main geometric characteristics of deformed sphere and standard spheroid
    Autorzy:
    Kovalchuk, Vasyl
    Mladenov, Ivaïlo M.
    Powiązania:
    https://bibliotekanauki.pl/articles/27311436.pdf
    Data publikacji:
    2023
    Wydawca:
    Polska Akademia Nauk. Czasopisma i Monografie PAN
    Tematy:
    deformed sphere
    standard spheroid
    sphericity index
    elliptic integrals
    elliptic functions
    tipping point
    bifurcation point
    sfera zdeformowana
    sferoida standardowa
    współczynnik sferyczności
    punkt zwrotny
    punkt bifurkacji
    całka eliptyczna
    funkcja eliptyczna
    Opis:
    In the paper we compare the geometric descriptions of the deformed sphere (i.e., the so-called λ-sphere) and the standard spheroid (namely, World Geodetic System 1984’s reference ellipsoid of revolution). Among the main geometric characteristics of those two surfaces of revolution embedded into the three-dimensional Euclidean space we consider the semi-major (equatorial) and semi-minor (polar) axes, quartermeridian length, surface area, volume, sphericity index, and tipping (bifurcation) point for geodesics. Next, the RMS (Root Mean Square) error is defined as the square-rooted arithmetic mean of the squared relative errors for the individual pairs of the discussed six main geometric characteristics. As a result of the process of minimization of the RMS error, we have obtained the proposition of the optimized value of the deformation parameter of the λ-sphere, for which we have calculated the absolute and relative errors for the individual pairs of the discussed main geometric characteristics of λ-sphere and standard spheroid (the relative errors are of the order of 10−6 – 10−9). Among others, it turns out that the value of the,sup> flattening factor of the spheroid is quite a good approximation for the corresponding value of the deformation parameter of the λ-sphere (the relative error is of the order of 10−4).
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2023, 71, 5; art. no. e147058
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A study of chaos for processes under small perturbations II : rigorous proof of chaos
    Autorzy:
    Oprocha, P.
    Wilczyński, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/255940.pdf
    Data publikacji:
    2010
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    distributional chaos
    isolating segments
    fixed point index
    bifurcation
    Opis:
    In the present paper we prove distributional chaos for the Poincaré map in the perturbed equation [formula]. Heteroclinic and homoclinic connections between two periodic solutions bifurcating from the stationary solution 0 present in the system when N = 0 are also discussed.
    Źródło:
    Opuscula Mathematica; 2010, 30, 1; 5-36
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Bifurcation in a nonlinear steady state system
    Autorzy:
    Wang, G. Q.
    Cheng, S. S.
    Powiązania:
    https://bibliotekanauki.pl/articles/255541.pdf
    Data publikacji:
    2010
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    bifurcation
    cellular neural network
    steady state
    Krasnoselsky fixed point theorem
    Opis:
    The steady state solutions of a nonlinear digital cellular neural network with ω neural units and a nonnegative variable parameter λ are sought. We show that λ = 1 is a critical value such that the qualitative behavior of our network changes. More specifically, when ω is odd, then for λ ∈ [0, 1), there is one positive and one negative steady state, and for λ ∈ [1, ∞), steady states cannot exist; while when ω is even, then for λ ∈ [0, 1), there is one positive and one negative steady state, and for λ = 1, there are no nontrivial steady states, and for λ ∈ (1, ∞), there are two fully oscillatory steady states. Furthermore, the number of existing nontrivial solutions cannot be improved. It is hoped that our results are of interest to digital neural network designers.
    Źródło:
    Opuscula Mathematica; 2010, 30, 3; 349-360
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The Mechanism of Transformation of Global Business Cycles into Dynamics of Regional Real Estate Markets
    Autorzy:
    Jakimowicz, A.
    Kulesza, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/1029167.pdf
    Data publikacji:
    2018-06
    Wydawca:
    Polska Akademia Nauk. Instytut Fizyki PAN
    Tematy:
    housing price dynamics
    structural transition
    cusp catastrophe
    critical point
    bifurcation set
    equilibrium surface
    Opis:
    The aim of this article is the identification of the occurrence mechanism of sudden quantitative changes in real-estate market prices, which were observed during the global financial crisis. Since such phenomena did not occur to such an intensity during previous crises, it can be assumed that a new economic dynamic type has emerged in real-estate markets. The most promising of the methods of studying such phenomena seems to be the bifurcation method and particularly the catastrophe theory. This study analyzes changes in the prices of residential property based on cusp catastrophes. Empirical data were fit to a stochastic cusp model to visualize the evolutionary path of real estate market. Two other popular models (linear and logistic) were also estimated to compare results. A comparative analysis proved that the cusp model can best explain structural price instabilities in real-estate markets. The results confirmed that the evolution of the real estate market combines two processes: long-term evolution in the area of non-degenerate stability and discontinuous changes in the area of degenerate stability. Structural changes take place in the system only in the area of degenerate stability. The theoretical and practical results show that the catastrophe theory may have predictive potential, which could support traditional methods of predicting changes on real estate markets.
    Źródło:
    Acta Physica Polonica A; 2018, 133, 6; 1351-1361
    0587-4246
    1898-794X
    Pojawia się w:
    Acta Physica Polonica A
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-8 z 8

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