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.