Opuscula Math.
26
, no. 3
(), 499-506
Opuscula Mathematica

On the asymptotics of the difference equation with a proportional delay

Abstract. 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.
Keywords: asymptotics of difference equations, approximation methods for dynamical systems.
Mathematics Subject Classification: 39A11, 37M99.