<abstract xmlns="http://www.w3.org/1999/xhtml">In the recent years, there has been a lot of interest in studying the global behavior of, the socalled, max-type difference equations; see, for example, [<xref ref-type="bibr" rid="j_amns.2020.1.00025_ref_001_w2aab3b7e1584b1b6b1ab2ab1Aa">1</xref>, <xref ref-type="bibr" rid="j_amns.2020.1.00025_ref_002_w2aab3b7e1584b1b6b1ab2ab2Aa">2</xref>, <xref ref-type="bibr" rid="j_amns.2020.1.00025_ref_003_w2aab3b7e1584b1b6b1ab2ab3Aa">3</xref>, <xref ref-type="bibr" rid="j_amns.2020.1.00025_ref_004_w2aab3b7e1584b1b6b1ab2ab4Aa">4</xref>, <xref ref-type="bibr" rid="j_amns.2020.1.00025_ref_005_w2aab3b7e1584b1b6b1ab2ab5Aa">5</xref>, <xref ref-type="bibr" rid="j_amns.2020.1.00025_ref_006_w2aab3b7e1584b1b6b1ab2ab6Aa">6</xref>, <xref ref-type="bibr" rid="j_amns.2020.1.00025_ref_007_w2aab3b7e1584b1b6b1ab2ab7Aa">7</xref>, <xref ref-type="bibr" rid="j_amns.2020.1.00025_ref_008_w2aab3b7e1584b1b6b1ab2ab8Aa">8</xref>, <xref ref-type="bibr" rid="j_amns.2020.1.00025_ref_009_w2aab3b7e1584b1b6b1ab2ab9Aa">9</xref>, <xref ref-type="bibr" rid="j_amns.2020.1.00025_ref_010_w2aab3b7e1584b1b6b1ab2ac10Aa">10</xref>, <xref ref-type="bibr" rid="j_amns.2020.1.00025_ref_011_w2aab3b7e1584b1b6b1ab2ac11Aa">11</xref>, <xref ref-type="bibr" rid="j_amns.2020.1.00025_ref_012_w2aab3b7e1584b1b6b1ab2ac12Aa">12</xref>, <xref ref-type="bibr" rid="j_amns.2020.1.00025_ref_013_w2aab3b7e1584b1b6b1ab2ac13Aa">13</xref>, <xref ref-type="bibr" rid="j_amns.2020.1.00025_ref_014_w2aab3b7e1584b1b6b1ab2ac14Aa">14</xref>, <xref ref-type="bibr" rid="j_amns.2020.1.00025_ref_015_w2aab3b7e1584b1b6b1ab2ac15Aa">15</xref>, <xref ref-type="bibr" rid="j_amns.2020.1.00025_ref_016_w2aab3b7e1584b1b6b1ab2ac16Aa">16</xref>, <xref ref-type="bibr" rid="j_amns.2020.1.00025_ref_017_w2aab3b7e1584b1b6b1ab2ac17Aa">17</xref>]. The study of max type difference equations has also attracted some attention recently. We study the behaviour of the solutions of the following system of difference equation with the max operator: paper deals with the behaviour of the solutions of the max type system of difference equations,
<disp-formula id="j_amns.2020.1.00025_eq_001_w2aab3b7e1584b1b6b1aab1c16b1c35Aa"><label>(1)</label><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_amns.2020.1.00025_eq_001.png"></graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mtable><mtr><mtd><mrow><msub><mi>x</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><mi mathvariant="italic">max</mi><mrow><mo>{</mo><mrow><mfrac><mi>A</mi><mrow><msub><mi>x</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow></mfrac><mo>,</mo><mfrac><mrow><msub><mi>y</mi><mi>n</mi></msub></mrow><mrow><msub><mi>x</mi><mi>n</mi></msub></mrow></mfrac></mrow><mo>}</mo></mrow><mo>;</mo></mrow></mtd><mtd><mrow><msub><mi>y</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><mi mathvariant="italic">max</mi><mrow><mo>{</mo><mrow><mfrac><mi>A</mi><mrow><msub><mi>y</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow></mfrac><mo>,</mo><mfrac><mrow><msub><mi>x</mi><mi>n</mi></msub></mrow><mrow><msub><mi>y</mi><mi>n</mi></msub></mrow></mfrac></mrow><mo>}</mo><mo>,</mo></mrow></mrow></mtd></mtr></mtable></mrow></math><tex-math>\matrix{ {x_{n + 1} = max \left\{ {{A \over {x_{n - 1} }},{{y_n } \over {x_n }}} \right\};} &amp; {y_{n + 1} = max \left\{ {{A \over {y_{n - 1} }},{{x_n } \over {y_n }}} \right\},}}</tex-math></alternatives></disp-formula>
where the parametr <italic>A</italic> and initial conditions <italic>x</italic>−1,<italic>x</italic>0, <italic>y</italic>−1,<italic>y</italic>0 are positive reel numbers.</abstract>

In the recent years, there has been a lot of interest in studying the global behavior of, the socalled, max-type difference equations; see, for example, [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]. The study of max type difference equations has also attracted some attention recently. We study the behaviour of the solutions of the following system of difference equation with the max operator: paper deals with the behaviour of the solutions of the max type system of difference equations,
(1)xn+1=max{Axn−1,ynxn};yn+1=max{Ayn−1,xnyn},\matrix{ {x_{n + 1} = max \left\{ {{A \over {x_{n - 1} }},{{y_n } \over {x_n }}} \right\};} & {y_{n + 1} = max \left\{ {{A \over {y_{n - 1} }},{{x_n } \over {y_n }}} \right\},}}
where the parametr A and initial conditions x−1,x0, y−1,y0 are positive reel numbers.

Solution of the Maximum of Difference Equation 
<inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_amns.2020.1.00025_ieq_001.png"/><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mtable><mtr><mtd><mrow><msub><mi>x</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><mi mathvariant="italic">max</mi><mrow><mo>{</mo><mrow><mfrac><mi>A</mi><mrow><msub><mi>x</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow></mfrac><mo>,</mo><mfrac><mrow><msub><mi>y</mi><mi>n</mi></msub></mrow><mrow><msub><mi>x</mi><mi>n</mi></msub></mrow></mfrac></mrow><mo>}</mo></mrow><mo>;</mo></mrow></mtd><mtd><mrow><msub><mi>y</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><mi mathvariant="italic">max</mi><mrow><mo>{</mo><mrow><mfrac><mi>A</mi><mrow><msub><mi>y</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow></mfrac><mo>,</mo><mfrac><mrow><msub><mi>x</mi><mi>n</mi></msub></mrow><mrow><msub><mi>y</mi><mi>n</mi></msub></mrow></mfrac></mrow><mo>}</mo></mrow></mrow></mtd></mtr></mtable></mrow></math><tex-math>\matrix{ {x_{n + 1} = max \left\{ {{A \over {x_{n - 1} }},{{y_n } \over {x_n }}} \right\};} &amp; {y_{n + 1} = max \left\{ {{A \over {y_{n - 1} }},{{x_n } \over {y_n }}} \right\}}}</tex-math></alternatives></inline-formula>

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

Solution of the Maximum of Difference Equation 


In the recent years, there has been a lot of interest in studying the global behavior of, the socalled, max-type difference equations; see, for example, [1, 2,...

Publié en ligne: 31 mars 2020

Pages: 275 - 282

Reçu: 21 mai 2019

Accepté: 09 oct. 2019

DOI: https://doi.org/10.2478/amns.2020.1.00025

Mots clés
Difference equations, Periodicity, Max type difference equations

© 2020 Dagistan Simsek et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Solution of the Maximum of Difference Equation xn+1=max{Axn−1,ynxn};yn+1=max{Ayn−1,xnyn}\matrix{ {x_{n + 1} = max \left\{ {{A \over {x_{n - 1} }},{{y_n } \over {x_n }}} \right\};} & {y_{n + 1} = max \left\{ {{A \over {y_{n - 1} }},{{x_n } \over {y_n }}} \right\}}}

Publié en ligne: 31 mars 2020

Pages: 275 - 282

Reçu: 21 mai 2019

Accepté: 09 oct. 2019

DOI: https://doi.org/10.2478/amns.2020.1.00025

Mots clésDifference equations, Periodicity, Max type difference equations

© 2020 Dagistan Simsek et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Mots clés
Difference equations, Periodicity, Max type difference equations