On the solutions of a max‐type difference equation system

Abstract

Communicated by Y. S. XuIn this paper, we study behavior of the solution of the following max-type difference equation system:where N 0 D N [ f0g , the parameter A is positive real number, and the initial values x 0 , y 0 are positive real numbers.

Global attractivity of a rational difference equation of order twenty

“…Difference equations are very simple in form but it is very difficult to understand the behavior of their solutions (Ahmed and Youssef, 2013;Alghamdi et al, 2013;Asiri et al, 2015;Das and Bayram, 2010;Din, 2015). Khaliq and Elsayed (2016) For other relevant work on difference equations see (Touafek and Haddad, 2015;Yazlik et al, 2014Yazlik et al, , 2015Zayed, 2014;Zhang et al, 2014). Suppose that is some interval of real numbers and a continuous function defined on +1 ( + 1 ), where is some natural number.…”

The Form of the Solutions of Nonlinear Difference Equations Systems

“…The subject of the qualitative study of the nonlinear delay population models is very extensive, and the current research work tends to center around the relevant global dynamics of the considered systems of difference equations such as oscillation, boundedness of solutions, persistence, global stability of positive steady states, permanence, and global existence of periodic solutions. See [1], [19], [22]- [50] and the references therein. In particular, Cinar [2] studied the periodicity of the positive solutions of the system of the difference equations x n+1 = 1 y n , y n+1 = y n x n−1 y n− 1 .…”

Eventually Periodic Solutions of a Max-Type System of Difference Equations of Higher Order

“…Yazlik et al [4] in 2015 obtained in an elegant way the general solution of (6). In 2014, Stević et al [5] investigated the behavior of positive solutions of the following max-type system of difference equations:…”