Sixth Mississippi State Conference on Differential Equations and Computational Simulations.
Electron. J. Diff. Eqns., Conference 15 (2007), pp. 229-238.

Global attractivity in a nonlinear difference equation

Chuanxi Qian, Yijun Sun

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.

Show me the PDF file (233K), TEX file, and other files for this article.

Chuanxi Qian
Department of Mathematics and Statistics
Mississippi State University
Mississippi State, MS 39762, USA
email: qian@math.msstate.edu
Yijun Sun
Department of Mathematics and Statistics
Mississippi State University
Mississippi State, MS 39762, USA
email: ys101@msstate.edu

Return to the table of contents for this conference.
Return to the EJDE web page