Opuscula Mathematica

Opuscula Math.
, 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.
Cite this article as:
Petr Kundrát, On the asymptotics of the difference equation with a proportional delay, Opuscula Math. 26, no. 3 (2006), 499-506
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ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
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