Local stability of period two cycles of second order rational difference equation

S. Atawna, R. Abu-Saris, Ishak Hashim

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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).

Original languageEnglish
Article number969813
JournalDiscrete Dynamics in Nature and Society
Volume2012
DOIs
Publication statusPublished - 2012

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Period Two Solutions
Rational Difference Equation
Second-order Difference Equations
Local Stability
Difference equations
Cycle
Asymptotically Stable
Initial conditions
Non-negative
Necessary Conditions
Sufficient Conditions

ASJC Scopus subject areas

  • Modelling and Simulation

Cite this

Local stability of period two cycles of second order rational difference equation. / Atawna, S.; Abu-Saris, R.; Hashim, Ishak.

In: Discrete Dynamics in Nature and Society, Vol. 2012, 969813, 2012.

Research output: Contribution to journalArticle

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