A period 5 difference equation

Kosmala, W.A.J.

doi:10.22075/ijnaa.2011.107

A period 5 difference equation

Document Type : Research Paper

Author

W.A.J. Kosmala

Department of Math. Sci., Appalachian State University, Boone, NC 28608, USA

10.22075/ijnaa.2011.107

Abstract

The main goal of this note is to introduce another second-order difference equation where every nontrivial solution is of minimal period 5, namely the difference equation:
$$x_{n+1} =\frac{1 + x_{n−1}}{x_nx_{n−1} − 1}, n = 1, 2, 3, . . .$$
with initial conditions $x_0$ and $x_1$ any real numbers such that $x_0x_1 \neq 1$.

Keywords

difference equation

periodicity

equilibrium points

convergence