Opuscula Math. 26, no. 3 (2006), 499-506

Opuscula Mathematica

On the asymptotics of the difference equation with a proportional delay

Petr Kundrát

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.

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  • Petr Kundrát
  • Brno University of Technology, Institute of Mathematics, Technická 2, 61669 Brno, Czech Republic
  • Received: 2005-10-03.
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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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