International Journal of Nonlinear Analysis and Applications

On the nature of solutions of the difference equation $\mathbf{x_{n+1}=x_{n}x_{n-3}-1}$

Document Type : Research Paper

Authors

1 Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, P. O. Box 842014, Richmond, Virginia 23284-2014 USA.

2 Department of Mathematical Sciences, Appalachian State University, Boone, North Carolina 28608 USA.

Abstract

We investigate the long-term behavior of solutions of the difference equation
$$x_{n+1}=x_{n}x_{n-3}-1,   n=0,1, \ldots $$
where the initial conditions $x_{-3} ,, x_{-2} ,, x_{-1} ,, x_{0}$ are real numbers.  In particular, we look at the periodicity and asymptotic periodicity of solutions, as well as the existence of unbounded solutions.

Keywords

International Journal of Nonlinear Analysis and Applications
Volume 2, Issue 2 - Serial Number 2
December 2011
Pages 24-43
  • Receive Date: 03 August 2011
  • Revise Date: 11 September 2011
  • Accept Date: 18 September 2011