Global Asymptotic Stability for a Fourth-Order Rational Difference Equation

Meseret Tuba Gülpinar and Mustafa Bayram

Discrete Dynamics in Nature and Society, 2009, vol. 2009, 1-7

Abstract:

Our aim is to investigate the global behavior of the following fourth-order rational difference equation: 𠑥 𠑛 + 1 = ( 𠑥 𠑛 𠑥 𠑛 − 2 𠑥 𠑛 − 3 + 𠑥 𠑛 + 𠑥 𠑛 − 2 + 𠑥 𠑛 − 3 + 𠑎 ) / ( 𠑥 𠑛 𠑥 𠑛 − 2 + 𠑥 𠑛 𠑥 𠑛 − 3 + 𠑥 𠑛 − 2 𠑥 𠑛 − 3 + 1 + 𠑎 ) , 𠑛 = 0 , 1 , 2 , … where 𠑎 ∈ [ 0 , ∞ ) and the initial values 𠑥 − 3 , 𠑥 − 2 , 𠑥 − 1 , 𠑥 0 ∈ ( 0 , ∞ ) . To verify that the positive equilibrium point of the equation is globally asymptotically stable, we used the rule of the successive lengths of positive and negative semicycles of nontrivial solutions of the aforementioned equation.

Date: 2009
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/DDNS/2009/616982.pdf (application/pdf)
http://downloads.hindawi.com/journals/DDNS/2009/616982.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:616982

DOI: 10.1155/2009/616982

Access Statistics for this article

More articles in Discrete Dynamics in Nature and Society from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().