On the Period-Two Cycles of xn+1=(α+βxn+γxn-k)/(A+Bxn+Cxn-k)
| Autor: | S. Atawna, R. Abu-Saris, I. Hashim, E. S. Ismail |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | Abstract and Applied Analysis, Vol 2013 (2013) |
| Druh dokumentu: | article |
| ISSN: | 1085-3375 1687-0409 |
| DOI: | 10.1155/2013/179423 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
| Externí odkaz: |
|