TY  - JOUR
ID  - Kundrát2006
LB  - Kundrát2006
AU  - Kundrát, Petr
TI  - On the asymptotics of the difference equation with a proportional delay
ST  - On the asymptotics of the difference equation with a proportional delay
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2006
VL  - 26
IS  - 3
SP  - 499
EP  - 506
DO  - http://dx.doi.org/10.7494/OpMath.2006.26.3.499
UR  - http://dx.doi.org/10.7494/OpMath.2006.26.3.499
AB  - 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.
KW  - asymptotics of difference equations
KW  - approximation methods for dynamical systems
SN  - 1232-9274
ER  -