Boundedness and Stability for Higher Order Difference Equations

Ulrich Krause, Mihály Pituk

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

Sufficient conditions are given under which the higher order difference equation Xn+1 = f(xn,xn-1,..., x n-k), n = 0, 1, 2,... generates an order preserving discrete dynamical system with respect to the discrete exponential ordering. It is shown that under the above monotonicity assumption the boundedness of all solutions as well as the local and global stability of an equilibrium hold if and only if they hold for the much simpler first order equation xn+1 = h(x n), where h(x) = f(x, x,..., x). As an application, a second order nonlinear difference equation from macroeconomics and a discrete analogue of a model of haematopoiesis are discussed.

Original languageEnglish
Pages (from-to)343-356
Number of pages14
JournalJournal of Difference Equations and Applications
Volume10
Issue number4
DOIs
Publication statusPublished - Apr 10 2004

Keywords

  • Boundedness
  • Discrete exponential ordering
  • Global asymptotic stability
  • Higher order difference equations
  • Local stability
  • Order preserving map

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics

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