On the asymptotic behavior and periodic nature of a difference equation with maximum

https://doi.org/10.1016/j.camwa.2009.10.004Get rights and content
Under an Elsevier user license
open archive

Abstract

In this paper, we investigate the asymptotic behavior and periodic nature of positive solutions of the difference equation xn=max{Axn1,1xn2α},n0, where A0 and 0α1. We prove that every positive solution of this difference equation approaches x¯=1 or is eventually periodic with a period 2, 3 or 4.

Keywords

Max operator
Difference equation
Positive solution
Global attractivity
Periodicity

Cited by (0)