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On the Period-Two Cycles of xn+1=(α+βxn+γxn-k)/(A+Bxn+Cxn-k)
oleh: S. Atawna, R. Abu-Saris, I. Hashim, E. S. Ismail
Format: | Article |
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Diterbitkan: | Wiley 2013-01-01 |
Deskripsi
We consider the higher order nonlinear rational difference equation xn+1=(α+βxn+γxn-k)/(A+Bxn+Cxn-k),n=0,1,2,…, where the parameters α,β,γ,A,B,C are positive real numbers and the initial conditions x-k,…,x-1,x0 are nonnegative real numbers, k∈{1,2,…}. 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.