Global stability for mixed monotone systems

Research output: Contribution to journalArticle

12 Citations (Scopus)

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 2008

Fingerprint

Monotone Systems
Global Stability
Convergence of numerical methods
Difference equations
Interval Order
Discrete Dynamics
Global Attractivity
Higher order equation
Decomposable
Difference equation
Immediately
Monotone
Invariant
Necessary
Series

Keywords

  • Global stability
  • Mixed monotone system
  • Monotone dynamical system

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics
  • Analysis

Cite this

Global stability for mixed monotone systems. / Smith, Hal.

In: Journal of Difference Equations and Applications, Vol. 14, No. 10-11, 10.2008, p. 1159-1164.

Research output: Contribution to journalArticle

@article{51f35b22deb247c2995c8a5bca7f3539,
title = "Global stability for mixed monotone systems",
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.",
keywords = "Global stability, Mixed monotone system, Monotone dynamical system",
author = "Hal Smith",
year = "2008",
month = "10",
doi = "10.1080/10236190802332126",
language = "English (US)",
volume = "14",
pages = "1159--1164",
journal = "Journal of Difference Equations and Applications",
issn = "1023-6198",
publisher = "Taylor and Francis Ltd.",
number = "10-11",

}

TY - JOUR

T1 - Global stability for mixed monotone systems

AU - Smith, Hal

PY - 2008/10

Y1 - 2008/10

N2 - 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.

AB - 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.

KW - Global stability

KW - Mixed monotone system

KW - Monotone dynamical system

UR - http://www.scopus.com/inward/record.url?scp=53349116672&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=53349116672&partnerID=8YFLogxK

U2 - 10.1080/10236190802332126

DO - 10.1080/10236190802332126

M3 - Article

AN - SCOPUS:53349116672

VL - 14

SP - 1159

EP - 1164

JO - Journal of Difference Equations and Applications

JF - Journal of Difference Equations and Applications

SN - 1023-6198

IS - 10-11

ER -