Global asymptotic behavior of a discrete system of difference equations with delays

Abstract

In the present paper, we mainly investigate the qualitative behavior of the solutions of a discrete system of difference equations

x_{n+1}=α+((∑_{i=1}^{m}x_{n-i})/(y_{n})),y_{n+1}=β+((∑_{i=1}^{m}y_{n-i})/(x_{n})), n∈N

where α,β∈(0,∞), m∈Z⁺, x_{-i} and y_{-i} are non-negative real numbers for i∈{0,1,…,m}. Namely, we discuss the boundedness character, the asymptotic stability properties of steady states of mentioned system. Finally, for this system, we give a rate of convergence result which has an important place in the discrete dynamical systems. Besides, some numerical simulations with graphs are given in order to emphasize the efficiency of our theoretical results in the article.