Eventual periodicity of a max-type system of difference equations of higher order with four variables

Abstract

The aim of this paper is to investigate eventual periodicity of the following max-type system of difference equations of higher order with four variableswhere k is a positive integer, A, B,C, D ∈ (0, +∞) with A ≤ B and C ≤ D, and the initial valuesn=−k of this system which is not eventually periodic.(2) If BD = AC = 1 with A ̸ = C or BD > AC = 1 or AC > 1, then every solution of this system is eventually periodic.