Global asymptotic stability in a perturbed higher-order linear difference equation

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In this note, we give a sufficient condition for the global asymptotic stability of the zero solution of the difference equation x(n + 1) = ∑i=0k pi(n)x(n-i)+f(n,x(n),x(n - 1),..., x(n - 1)), n = 0,1,..., where k and l are nonnegative integers, the coefficients pi(n) are real numbers, and the nonlinearity f satisfies the growth condition |f(n,x0,x1,...,xl)| ≤ q max/0 ≤i≤ l |xi|, for n = 0,1,... and xi ε ℝ, 0 ≤ i ≤ l, where q is a constant. The stability condition is formulated in terms of the fundamental solution of the unperturbed equation y(n + 1) = ∑i=0k Pi(n)y(n - i).

Original languageEnglish
Pages (from-to)1195-1202
Number of pages8
JournalComputers and Mathematics with Applications
Issue number6-9
Publication statusPublished - Mar 1 2003


  • Difference equation
  • Global asymptotic stability
  • Perturbed equation

ASJC Scopus subject areas

  • Modelling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

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