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Global Asymptotic Stability of a Rational System

Global asymptotic stability of a rational system
descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Jan 2014 English Publisher:WileyJournal:Abstract and Applied Analysis, volume 2,014, pages 1-6 (issn: 1085-3375, eissn: 1687-0409, Copyright policy )
Authors: Lin-Xia Hu; Xiu-Mei Jia;

doi: 10.1155/2014/286375

Global Asymptotic Stability of a Rational System

Abstract

The main goal of this paper is to investigate the global asymptotic behavior of the difference equationxn+1=β1xn/A1+yn,yn+1=β2xn+γ2yn/xn+yn,n=0,1,2,…withβ1,β2,γ2,A1∈(0,∞)and the initial value(x0,y0)∈[0,∞)×[0,∞)such thatx0+y0≠0. The major conclusion shows that, in the case whereγ2<β2, if the unique positive equilibrium(x-,y-)exists, then it is globally asymptotically stable.

Related Organizations
Keywords

global asymptotic behavior, asymptotic stability, Stability theory for difference equations, QA1-939, Mathematics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
3
Average
Average
Average
gold