Qualitative behavior of two systems of higher‐order difference equations

Abstract

In this paper, we study the qualitative behavior of following two systems of higher‐order difference equations: urn:x-wiley:mma:media:mma3752:mma3752-math-0001 and urn:x-wiley:mma:media:mma3752:mma3752-math-0002 where the parameters α,β,γ,α1,β1,γ1,a,b,c,a1,b1,andc1 and the initial conditions x0, x−1, ⋯, x−k, y0, y−1 ,⋯, y−k are positive real numbers. More precisely, we study the equilibrium points, local asymptotic stability, instability, global asymptotic stability of equilibrium points, and rate of convergence of positive solutions that converges to the equilibrium point P0=(0,0) of these systems. Some numerical examples are given to verify our theoretical results. These examples are experimental verification of our theoretical discussions. Copyright © 2015 John Wiley & Sons, Ltd.