Global attractivity of the equilibrium of a nonlinear difference equation

Graef, John R., and Qian, C.. "Global attractivity of the equilibrium of a nonlinear difference equation." Czechoslovak Mathematical Journal 52.4 (2002): 757-769. <http://eudml.org/doc/30742>.

@article{Graef2002,
abstract = {The authors consider the nonlinear difference equation \[ x\_\{n+1\}=\alpha x\_n + x\_\{n-k\}f(x\_\{n-k\}), \quad n=0, 1,\dots .1 \text\{where\} \alpha \in (0, 1),\hspace\{5.0pt\}k \in \lbrace 0, 1, \dots \rbrace \hspace\{5.0pt\}\text\{and\}\hspace\{5.0pt\}f\in C^1[[0, \infty ),[0, \infty )] \qquad \mathrm \{(0)\}\] with $f^\{\prime \}(x)<0$. They give sufficient conditions for the unique positive equilibrium of (0.1) to be a global attractor of all positive solutions. The results here are somewhat easier to apply than those of other authors. An application to a model of blood cell production is given.},
author = {Graef, John R., Qian, C.},
journal = {Czechoslovak Mathematical Journal},
keywords = {nonlinear difference equation; global attractivity; oscillation; nonlinear difference equation; global attractivity; oscillation; positive equilibrium; positive solutions; blood cell production},
language = {eng},
number = {4},
pages = {757-769},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Global attractivity of the equilibrium of a nonlinear difference equation},
url = {http://eudml.org/doc/30742},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Graef, John R.
AU - Qian, C.
TI - Global attractivity of the equilibrium of a nonlinear difference equation
JO - Czechoslovak Mathematical Journal
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 4
SP - 757
EP - 769
AB - The authors consider the nonlinear difference equation \[ x_{n+1}=\alpha x_n + x_{n-k}f(x_{n-k}), \quad n=0, 1,\dots .1 \text{where} \alpha \in (0, 1),\hspace{5.0pt}k \in \lbrace 0, 1, \dots \rbrace \hspace{5.0pt}\text{and}\hspace{5.0pt}f\in C^1[[0, \infty ),[0, \infty )] \qquad \mathrm {(0)}\] with $f^{\prime }(x)<0$. They give sufficient conditions for the unique positive equilibrium of (0.1) to be a global attractor of all positive solutions. The results here are somewhat easier to apply than those of other authors. An application to a model of blood cell production is given.
LA - eng
KW - nonlinear difference equation; global attractivity; oscillation; nonlinear difference equation; global attractivity; oscillation; positive equilibrium; positive solutions; blood cell production
UR - http://eudml.org/doc/30742
ER -