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    Wyświetlanie 1-3 z 3
    Tytuł:
    An unconditionally positive and global stability preserving NSFD scheme for an epidemic model with vaccination
    Autorzy:
    Ding, D.
    Ma, Q.
    Ding, X.
    Powiązania:
    https://bibliotekanauki.pl/articles/330497.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    nonstandard finite difference
    unconditional positivity
    stability
    Lyapunov function
    metoda różnic skończonych
    stabilność
    funkcja Lyapunova
    Opis:
    In this paper, a NonStandard Finite Difference (NSFD) scheme is constructed, which can be used to determine numerical solutions for an epidemic model with vaccination. Here the NSFD method is employed to derive a set of difference equations for the epidemic model with vaccination. We show that difference equations have the same dynamics as the original differential system, such as the positivity of the solutions and the stability of the equilibria, without being restricted by the time step. Our proof of global stability utilizes the method of Lyapunov functions. Numerical simulation illustrates the effectiveness of our results.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2014, 24, 3; 635-646
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Generalized practical stability analysis of discontinuous dynamical systems
    Autorzy:
    Zhai, G.
    Michel, A. N.
    Powiązania:
    https://bibliotekanauki.pl/articles/907305.pdf
    Data publikacji:
    2004
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    układ dynamiczny nieciągły
    analiza ilościowa
    funkcja Lyapunova
    discontinuous dynamical system
    quantitative analysis
    generalized practical stability
    Lyapunov-like function
    Opis:
    In practice, one is not only interested in the qualitative characterizations provided by the Lyapunov stability, but also in quantitative information concerning the system behavior, including estimates of trajectory bounds, possibly over finite time intervals. This type of information has been ascertained in the past in a systematic manner using the concept of practical stability. In the present paper, we give a new definition of generalized practical stability (abbreviated as GP-stability) and establish some sufficient conditions concerning GP-stability for a wide class of discontinuous dynamical systems. As in the classical Lyapunov theory, our results constitute a Direct Method, making use of auxiliary scalar-valued Lyapunov-like functions. These functions, however, have properties that differ significantly from the usual Lyapunov functions. We demonstrate the applicability of our results by means of several specific examples.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2004, 14, 1; 5-12
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Convergence method, properties and computational complexity for Lyapunov games
    Autorzy:
    Clempner, J. B.
    Poznyak, A. S.
    Powiązania:
    https://bibliotekanauki.pl/articles/907787.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    punkt równowagi Lyapunova
    funkcja Lapunowa
    proces decyzyjny
    Lyapunov game
    Lyapunov equilibrium point
    best reply
    repeated games
    forward decision process
    Opis:
    We introduce the concept of a Lyapunov game as a subclass of strictly dominated games and potential games. The advantage of this approach is that every ergodic system (repeated game) can be represented by a Lyapunov-like function. A direct acyclic graph is associated with a game. The graph structure represents the dependencies existing between the strategy profiles. By definition, a Lyapunov-like function monotonically decreases and converges to a single Lyapunov equilibrium point identified by the sink of the game graph. It is important to note that in previous works this convergence has not been guaranteed even if the Nash equilibrium point exists. The best reply dynamics result in a natural implementation of the behavior of a Lyapunov-like function. Therefore, a Lyapunov game has also the benefit that it is common knowledge of the players that only best replies are chosen. By the natural evolution of a Lyapunov-like function, no matter what, a strategy played once is not played again. As a construction example, we show that, for repeated games with bounded nonnegative cost functions within the class of differentiable vector functions whose derivatives satisfy the Lipschitz condition, a complex vector-function can be built, where each component is a function of the corresponding cost value and satisfies the condition of the Lyapunov-like function. The resulting vector Lyapunov-like function is a monotonic function which can only decrease over time. Then, a repeated game can be represented by a one-shot game. The functionality of the suggested method is successfully demonstrated by a simulated experiment.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2011, 21, 2; 349-361
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-3 z 3

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