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On the behavior of solutions of the system of rational difference equations <inline-formula><m:math name="1687-1847-2011-40-i1" xmlns:m="http://www.w3.org/1998/Math/MathML"><m:msub> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo class="MathClass-bin">+</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo class="MathClass-rel">=</m:mo> <m:mfrac> <m:mrow> <m:msub> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo class="MathClass-bin">-</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msub> </m:mrow> <m:mrow> <m:msub> <m:mrow> <m:mi>y</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msub> <m:msub> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo class="MathClass-bin">-</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo class="MathClass-bin">-</m:mo> <m:mn>1</m:mn> </m:mrow> </m:mfrac> <m:mo class="MathClass-punc">,</m:mo> <m:mspace width="1em" class="quad"/> <m:msub> <m:mrow> <m:mi>y</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo class="MathClass-bin">+</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo class="MathClass-rel">=</m:mo> <m:mfrac> <m:mrow> <m:msub> <m:mrow> <m:mi>y</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo class="MathClass-bin">-</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msub> </m:mrow> <m:mrow> <m:msub> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msub> <m:msub> <m:mrow> <m:mi>y</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo class="MathClass-bin">-</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo class="MathClass-bin">-</m:mo> <m:mn>1</m:mn> </m:mrow> </m:mfrac> <m:mo class="MathClass-punc">,</m:mo> <m:mspace width="1em" class="quad"/> <m:msub> <m:mrow> <m:mi>z</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo class="MathClass-bin">+</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo class="MathClass-rel">=</m:mo> <m:mfrac> <m:mrow> <m:mn>1</m:mn> </m:mrow> <m:mrow> <m:msub> <m:mrow> <m:mi>y</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msub> <m:msub> <m:mrow> <m:mi>z</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msub> </m:mrow> </m:mfrac> </m:math> </inline-formula>
Published 2011-01-01“…<p>Abstract</p> <p>In this article, we investigate the solutions of the system of difference equations <inline-formula><m:math name="1687-1847-2011-40-i2" xmlns:m="http://www.w3.org/1998/Math/MathML"><m:msub> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo class="MathClass-bin">+</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo class="MathClass-rel">=</m:mo> <m:mfrac> <m:mrow> <m:msub> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo class="MathClass-bin">-</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msub> </m:mrow> <m:mrow> <m:msub> <m:mrow> <m:mi>y</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msub> <m:msub> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo class="MathClass-bin">-</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo class="MathClass-bin">-</m:mo> <m:mn>1</m:mn> </m:mrow> </m:mfrac> </m:math> </inline-formula>, <inline-formula><m:math name="1687-1847-2011-40-i3" xmlns:m="http://www.w3.org/1998/Math/MathML"><m:msub> <m:mrow> <m:mi>y</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo class="MathClass-bin">+</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo class="MathClass-rel">=</m:mo> <m:mfrac> <m:mrow> <m:msub> <m:mrow> <m:mi>y</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo class="MathClass-bin">-</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msub> </m:mrow> <m:mrow> <m:msub> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msub> <m:msub> <m:mrow> <m:mi>y</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo class="MathClass-bin">-</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo class="MathClass-bin">-</m:mo> <m:mn>1</m:mn> </m:mrow> </m:mfrac> </m:math> </inline-formula>, <inline-formula><m:math name="1687-1847-2011-40-i4" xmlns:m="http://www.w3.org/1998/Math/MathML"><m:msub> <m:mrow> <m:mi>z</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo class="MathClass-bin">+</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo class="MathClass-rel">=</m:mo> <m:mfrac> <m:mrow> <m:mn>1</m:mn> </m:mrow> <m:mrow> <m:msub> <m:mrow> <m:mi>y</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msub> <m:msub> <m:mrow> <m:mi>z</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msub> </m:mrow> </m:mfrac> </m:math> </inline-formula> where <it>x</it><sub>0</sub>, <it>x</it><sub>-1</sub>, <it>y</it><sub>0</sub>, <it>y</it><sub>-1</sub>, <it>z</it><sub>0</sub>, <it>z</it><sub>-1</sub> real numbers such that <it>y</it><sub>0</sub><it>x</it><sub>-1</sub> ≠ 1, <it>x</it><sub>0</sub><it>y</it><sub>-1</sub> ≠ 1 and <it>y</it><sub>0</sub><it>z</it><sub>0</sub> ≠ 0.…”
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