The authors study the global behavior of the difference equation
where , , , are positive constants and the initial conditions , , are nonnegative. The case where was studied by M. R. S. Kulenović, G. Ladas and N. R. Prokup [Comput. Math. Appl. 41, No. 5–6, 671–678 (2001; Zbl 0985.39017)].
A certain change of variable is given to simplify the equations. It is shown that zero is always an equilibrium point which satisfies a necessary and suffient condition for its local asymptotic stability. With a specific assumption on the parameters, there is a unique positive equilibrium point whose global stability is discussed. The authors examine the nature of semicycles of solutions and discuss invariant intervals.