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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
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 $$a>b$$.

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