On global behavior of a system of nonlinear difference equations of order two. (English) Zbl 1377.39006

Tollu, D. T.; Yazlik, Y.; Taskara, N.

Adv. Stud. Contemp. Math., Kyungshang 27, No. 3, 373-383 (2017).

Summary: In this paper we deal with the system of difference equations \[ x_{n+1}= {a\over 1+ x_n y_{n-1}},\;y_{n+1}= {b\over 1+ y_n x_{n-1}},\quad n\in\mathbb{N}_0, \] where the parameters \(a\), \(b\) are positive real numbers and the initial conditions \(x_{-1}\), \(x_0\), \(y_{-1}\), \(y_0\) are nonnegative real numbers. We study global behavior of the above system.
Also, we give rate of convergence of the solution which tends to unique positive equilibrium point of the system and illustrate our theoretical results by means of some numerical examples.

MSC:

39A10

Additive difference equations

Keywords:

equilibrium point; global asymptotic stability; nonlinear difference equation; periodic solution; rate of convergence