On a third-order system of difference equations

Abstract

We show that the system of difference equationsxn+ 1= a1xn- 2b1ynzn- 1xn- 2+ c1,yn+ 1= a2yn- 2b2znxn- 1yn- 2+ c2,zn+ 1= a3zn- 2b3xnyn- 1zn- 2+ c3,n∈ N0,where the parameters ai, bi, ci,i∈{1,2,3}, and initial values x- j,y- j,z- j,j∈{0,1,2}, are real numbers, can be solved, developing further the results in the literature.