On the system of rational difference equations \(x_n=a/y_{n-3}\), \(y_n=by_{n-3}/x_{n-q}y_{n-q}\). (English) Zbl 1123.39006

Özban, Ahmet Yaşar

Appl. Math. Comput. 188, No. 1, 833-837 (2007).

The author studies the system of rational difference equation \[ x_n=a/y_{n-3}, \quad y_n=by_{n-3}/x_{n-q}y_{n-q}, \;n=1,2,\dots, \] where \(q>3\) is an integer and is not an integer multiple of \(3\), \(a\) and \(b\) are positive constants, and the initial values \(x_{-q+1}, x_{-q+2},\dots, x_0, y_{-q+1}, y_{-q+2},\dots,y_0\) are positive real numbers. Results are obtained on the behavior of the solutions \(\{(x_n,y_n)\}_{n=-(q-1)}^{\infty}\) for the cases when \(a=b, a<b\), and \(a>b\).

Reviewer: Qingkai Kong (DeKalb)

MSC:

39A11	Stability of difference equations (MSC2000)
39A20	Multiplicative and other generalized difference equations, e.g., of Lyness type

Keywords:

system of rational difference equation; positive solutions; eventually periodic solutions

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