Global behavior of a three-dimensional linear fractional system of difference equations

Abstract

We investigate the global asymptotic behavior of solutions of the system of difference equations x n + 1 = a + x n b + y n , y n + 1 = c + y n d + z n , z n + 1 = e + z n f + x n , n = 0 , 1 , … , where the parameters a, b, c, d, e, and f are in ( 0 , ∞ ) and the initial conditions x 0 , y 0 , and z 0 are arbitrary non-negative numbers. We obtain some global attractivity results for the positive equilibrium of this system for different values of the parameters.