Global stability for mixed monotone systems

Hal Smith

Research output: Contribution to journalArticle

14 Scopus citations

Abstract

We show that the embedding method described in J.-L. Gouze and P. Hadeler (Monotone flows and order intervals, Nonlinear World 1 (1994), pp. 23-34) and H.L. Smith (The discrete dynamics of monotonically decomposable maps, J. Math. Biol. 53 (2006), pp. 747-758) leads immediately to the global stability results in M. Kulenovic and O. Merino (A global attractivity result for maps with invariant boxes. Discrete Contin. Dyn. Syst. Series. B, 6 (2006), pp. 97-110). This allows the extension of some results on global stability for higher order difference equations due to Gerry Ladas and collaborators. Further, we provide a new result suggests that embedding into monotone systems may not be necessary for global stability results.

Original languageEnglish (US)
Pages (from-to)1159-1164
Number of pages6
JournalJournal of Difference Equations and Applications
Volume14
Issue number10-11
DOIs
StatePublished - Oct 1 2008

Keywords

  • Global stability
  • Mixed monotone system
  • Monotone dynamical system

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics

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