On the global behavior of the nonlinear difference equation xn+1=f(pn,xn−m,xn−t(k+1)+1)
We consider the following nonlinear difference equation: xn+1=f(pn,xn−m,xn−t(k+1)+1), n=0,1,2,…, where m∈{0,1,2,…} and k,t∈{1,2,…} with 0≤m<t(k+1)−1, the initial values x−t(k+1)+1,x−t(k+1)+2,…,x0∈(0,+∞), and {pn}n=0∞ is a positive sequence of the period k+1. We give sufficient conditions under wh...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2006-01-01
|
| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/DDNS/2006/90625 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | We consider the following nonlinear difference equation:
xn+1=f(pn,xn−m,xn−t(k+1)+1), n=0,1,2,…, where m∈{0,1,2,…} and
k,t∈{1,2,…} with 0≤m<t(k+1)−1, the initial
values x−t(k+1)+1,x−t(k+1)+2,…,x0∈(0,+∞),
and {pn}n=0∞ is a positive sequence of the period
k+1. We give sufficient conditions under which every positive
solution of this equation tends to the period k+1 solution. |
|---|---|
| ISSN: | 1026-0226 1607-887X |