Asymptotic Properties of Solutions of the Difference Equation deltax(t) = –ax(t) + bx(tau(t))

Abstract In this paper, we derive the asymptotic bounds of all solutions of the delay difference equation

∆x(t) = −ax(t) + bx(τ(t)), t ∈ [t0,∞)

with real constants a > 0, b 6= 0. This equation is obtained via the discretization of a delay differential equation and we show the resemblance in the asymptotic bounds of both equations.