Global Behavior of xn+1=(α+βxn-k)/(γ+xn)

Global Behavior of xn+1=(α+βxn-k)/(γ+xn)

This paper aims to investigate the global stability of negative solutions of the difference equation xn+1=(α+βxn-k)/(γ+xn), n=0,1,2,…, where the initial conditions x-k,…,x0∈-∞,0, k is a positive integer, and the parameters β,  γ0. By utilizing the invariant interval and periodic character of solutio...

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Veröffentlicht in:Discrete dynamics in nature and society 2013-01, Vol.2013 (2013), p.1-5
Hauptverfasser: Gan, Chenquan, Yang, Xiaofan, Zhang, Chunming
Format: Artikel
Sprache:eng
Schlagworte:
Asymptotic properties
Difference equations
Dynamics
Initial conditions
Integers
Intervals
Invariants
Stability
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Beschreibung
Zusammenfassung:This paper aims to investigate the global stability of negative solutions of the difference equation xn+1=(α+βxn-k)/(γ+xn), n=0,1,2,…, where the initial conditions x-k,…,x0∈-∞,0, k is a positive integer, and the parameters β,  γ0. By utilizing the invariant interval and periodic character of solutions, it is found that the unique negative equilibrium is globally asymptotically stable under some parameter conditions. Additionally, two examples are given to illustrate the main results in the end.
ISSN:1026-0226
1607-887X
DOI:10.1155/2013/963757