Local Stability of Period Two Cycles of Second Order Rational Difference Equation
Joint Authors
Abu-Saris, Raghib
Hashim, Ishak
Atawna, S.
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-11-22
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
We consider the second order rational difference equation xn+1=(α+βxn+γxn-1)/(A+Bxn+Cxn-1), n = 0,1,2,…, where the parameters α,β,γ,A,B,C are positive real numbers, and the initial conditions x-1,x0 are nonnegative real numbers.
We give a necessary and sufficient condition for the equation to have a prime period-two solution.
We show that the period-two solution of the equation is locally asymptotically stable.
In particular, we solve Conjecture 5.201.2 proposed by Camouzis and Ladas in their book (2008) which appeared previously in Conjecture 11.4.3 in Kulenović and Ladas monograph (2002).
American Psychological Association (APA)
Atawna, S.& Abu-Saris, Raghib& Hashim, Ishak. 2012. Local Stability of Period Two Cycles of Second Order Rational Difference Equation. Discrete Dynamics in Nature and Society،Vol. 2012, no. 2012, pp.1-11.
https://search.emarefa.net/detail/BIM-512306
Modern Language Association (MLA)
Atawna, S.…[et al.]. Local Stability of Period Two Cycles of Second Order Rational Difference Equation. Discrete Dynamics in Nature and Society No. 2012 (2012), pp.1-11.
https://search.emarefa.net/detail/BIM-512306
American Medical Association (AMA)
Atawna, S.& Abu-Saris, Raghib& Hashim, Ishak. Local Stability of Period Two Cycles of Second Order Rational Difference Equation. Discrete Dynamics in Nature and Society. 2012. Vol. 2012, no. 2012, pp.1-11.
https://search.emarefa.net/detail/BIM-512306
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-512306