Sixth Mississippi State Conference on Differential Equations and
Computational Simulations.
Electronic Journal of Differential Equations,
Conference 15 (2007), pp. 229-238. 

Title: Global attractivity in a nonlinear difference equation

Authors: Chuanxi Qian (Mississippi State Univ., MS, USA)
         Yijun Sun    (Mississippi State Univ., MS, USA)
 
Abstract: 
 In this paper, we study the asymptotic behavior of positive
 solutions of the nonlinear difference equation
 $$
 x_{n+1}=x_n f(x_{n-k}),
 $$
 where $f:[0,\infty)\to(0, \infty)$  is a unimodal
 function, and $k$ is a nonnegative integer. Sufficient
 conditions for the positive equilibrium to be a global attractor
 of all positive solutions are established. Our results can be
 applied to to some difference equations derived from mathematical
 biology.

Published February 28, 2007.
Math Subject Classifications: 39A10.
Key Words: Nonlinear difference equation; global attractor; 
           unimodal function; positive equilibrium.