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Browsing by Subject "approximation methods for dynamical systems"

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    Item type:Article, Access status: Open Access ,
    On the asymptotics of the difference equation with a proportional delay
    (2006) Kundrát, Petr
    This paper deals with asymptotic properties of a vector difference equation with delayed argument $\Delta x_k=Ax_k+Bx_{\lfloor\lambda k\rfloor},\qquad 0\lt\lambda\lt 1,\quad k=0,1,2,\dots,$ where $A$, $B$ are constant matrices and the term $\lfloor\lambda k\rfloor$ is the integer part of $\lambda k$. Our aim is to emphasize some resemblances between the asymptotic behaviour of this delay difference equation and its continuous counterpart.