Closed form expression of tractable semi-max-type two-dimensional system of difference equations with variable coefficients

Author

Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt

10.1016/j.joems.2016.03.002

Abstract

In this paper we shall examine the periodicity and formularization of the solutions for a
system of semi-max-type difference equations of second order in the form
x n +1 = max

A n
y n −1
, x n −1

,
y n +1 = min

B n
x n −1
, y n −1

,
n ∈ N 0 , where N 0 = N ∪ { 0 } , (A n ) n ∈ N 0 and (B n ) n ∈ N 0 are two-periodic positive sequences, and initial
values x 0 , x −1 , y 0 , y −1 ∈ (0 , + ∞ ) .

Keywords