Global and Local Behavior of the System of Piecewise Linear Difference Equations <i>x</i><sub><i>n</i>+1</sub> = |<i>x</i><sub><i>n</i></sub>| − <i>y</i><sub><i>n</i></sub> − <i>b</i> and <i>y</i><sub><i>n</i>+1</sub> = <i>x</i><sub><i>n</i></sub> − |<i>y</i><sub><i>n</i></sub>| + 1 Where <i>b</i> ≥ 4
The aim of this article is to study the system of piecewise linear difference equations <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>x</mi><mrow><mi>n</mi>&...
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MDPI AG
2021-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/12/1390 |
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| author | Busakorn Aiewcharoen Ratinan Boonklurb Nanthiya Konglawan |
| author_facet | Busakorn Aiewcharoen Ratinan Boonklurb Nanthiya Konglawan |
| author_sort | Busakorn Aiewcharoen |
| collection | DOAJ |
| description | The aim of this article is to study the system of piecewise linear difference equations <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>x</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><mrow><mo>|</mo><msub><mi>x</mi><mi>n</mi></msub><mo>|</mo></mrow><mo>−</mo><msub><mi>y</mi><mi>n</mi></msub><mo>−</mo><mi>b</mi></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>y</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><msub><mi>x</mi><mi>n</mi></msub><mo>−</mo><mrow><mo>|</mo><msub><mi>y</mi><mi>n</mi></msub><mo>|</mo></mrow><mo>+</mo><mn>1</mn></mrow></semantics></math></inline-formula> where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>≥</mo><mn>0</mn></mrow></semantics></math></inline-formula>. A global behavior for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>b</mi><mo>=</mo><mn>4</mn></mrow></semantics></math></inline-formula> shows that all solutions become the equilibrium point. For a large value of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>|</mo></mrow><msub><mi>x</mi><mn>0</mn></msub><mrow><mo>|</mo></mrow></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>|</mo></mrow><msub><mi>y</mi><mn>0</mn></msub><mrow><mo>|</mo></mrow></mrow></semantics></math></inline-formula>, we can prove that (i) if <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>b</mi><mo>=</mo><mn>5</mn></mrow></semantics></math></inline-formula>, then the solution becomes the equilibrium point and (ii) if <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>b</mi><mo>≥</mo><mn>6</mn></mrow></semantics></math></inline-formula>, then the solution becomes the periodic solution of prime period 5. |
| first_indexed | 2024-03-10T10:23:04Z |
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| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T10:23:04Z |
| publishDate | 2021-06-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj.art-1032f4bfe456443e963d85454bcbdfb72023-11-22T00:11:55ZengMDPI AGMathematics2227-73902021-06-01912139010.3390/math9121390Global and Local Behavior of the System of Piecewise Linear Difference Equations <i>x</i><sub><i>n</i>+1</sub> = |<i>x</i><sub><i>n</i></sub>| − <i>y</i><sub><i>n</i></sub> − <i>b</i> and <i>y</i><sub><i>n</i>+1</sub> = <i>x</i><sub><i>n</i></sub> − |<i>y</i><sub><i>n</i></sub>| + 1 Where <i>b</i> ≥ 4Busakorn Aiewcharoen0Ratinan Boonklurb1Nanthiya Konglawan2The Demonstration School of Silpakorn University, Faculty of Education, Silpakorn University, Nakhon Pathom 73000, ThailandDepartment of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, ThailandDepartment of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, ThailandThe aim of this article is to study the system of piecewise linear difference equations <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>x</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><mrow><mo>|</mo><msub><mi>x</mi><mi>n</mi></msub><mo>|</mo></mrow><mo>−</mo><msub><mi>y</mi><mi>n</mi></msub><mo>−</mo><mi>b</mi></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>y</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><msub><mi>x</mi><mi>n</mi></msub><mo>−</mo><mrow><mo>|</mo><msub><mi>y</mi><mi>n</mi></msub><mo>|</mo></mrow><mo>+</mo><mn>1</mn></mrow></semantics></math></inline-formula> where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>≥</mo><mn>0</mn></mrow></semantics></math></inline-formula>. A global behavior for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>b</mi><mo>=</mo><mn>4</mn></mrow></semantics></math></inline-formula> shows that all solutions become the equilibrium point. For a large value of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>|</mo></mrow><msub><mi>x</mi><mn>0</mn></msub><mrow><mo>|</mo></mrow></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>|</mo></mrow><msub><mi>y</mi><mn>0</mn></msub><mrow><mo>|</mo></mrow></mrow></semantics></math></inline-formula>, we can prove that (i) if <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>b</mi><mo>=</mo><mn>5</mn></mrow></semantics></math></inline-formula>, then the solution becomes the equilibrium point and (ii) if <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>b</mi><mo>≥</mo><mn>6</mn></mrow></semantics></math></inline-formula>, then the solution becomes the periodic solution of prime period 5.https://www.mdpi.com/2227-7390/9/12/1390equilibrium pointperiodic solutionsystem of piecewise linear difference equation |
| spellingShingle | Busakorn Aiewcharoen Ratinan Boonklurb Nanthiya Konglawan Global and Local Behavior of the System of Piecewise Linear Difference Equations <i>x</i><sub><i>n</i>+1</sub> = |<i>x</i><sub><i>n</i></sub>| − <i>y</i><sub><i>n</i></sub> − <i>b</i> and <i>y</i><sub><i>n</i>+1</sub> = <i>x</i><sub><i>n</i></sub> − |<i>y</i><sub><i>n</i></sub>| + 1 Where <i>b</i> ≥ 4 Mathematics equilibrium point periodic solution system of piecewise linear difference equation |
| title | Global and Local Behavior of the System of Piecewise Linear Difference Equations <i>x</i><sub><i>n</i>+1</sub> = |<i>x</i><sub><i>n</i></sub>| − <i>y</i><sub><i>n</i></sub> − <i>b</i> and <i>y</i><sub><i>n</i>+1</sub> = <i>x</i><sub><i>n</i></sub> − |<i>y</i><sub><i>n</i></sub>| + 1 Where <i>b</i> ≥ 4 |
| title_full | Global and Local Behavior of the System of Piecewise Linear Difference Equations <i>x</i><sub><i>n</i>+1</sub> = |<i>x</i><sub><i>n</i></sub>| − <i>y</i><sub><i>n</i></sub> − <i>b</i> and <i>y</i><sub><i>n</i>+1</sub> = <i>x</i><sub><i>n</i></sub> − |<i>y</i><sub><i>n</i></sub>| + 1 Where <i>b</i> ≥ 4 |
| title_fullStr | Global and Local Behavior of the System of Piecewise Linear Difference Equations <i>x</i><sub><i>n</i>+1</sub> = |<i>x</i><sub><i>n</i></sub>| − <i>y</i><sub><i>n</i></sub> − <i>b</i> and <i>y</i><sub><i>n</i>+1</sub> = <i>x</i><sub><i>n</i></sub> − |<i>y</i><sub><i>n</i></sub>| + 1 Where <i>b</i> ≥ 4 |
| title_full_unstemmed | Global and Local Behavior of the System of Piecewise Linear Difference Equations <i>x</i><sub><i>n</i>+1</sub> = |<i>x</i><sub><i>n</i></sub>| − <i>y</i><sub><i>n</i></sub> − <i>b</i> and <i>y</i><sub><i>n</i>+1</sub> = <i>x</i><sub><i>n</i></sub> − |<i>y</i><sub><i>n</i></sub>| + 1 Where <i>b</i> ≥ 4 |
| title_short | Global and Local Behavior of the System of Piecewise Linear Difference Equations <i>x</i><sub><i>n</i>+1</sub> = |<i>x</i><sub><i>n</i></sub>| − <i>y</i><sub><i>n</i></sub> − <i>b</i> and <i>y</i><sub><i>n</i>+1</sub> = <i>x</i><sub><i>n</i></sub> − |<i>y</i><sub><i>n</i></sub>| + 1 Where <i>b</i> ≥ 4 |
| title_sort | global and local behavior of the system of piecewise linear difference equations i x i sub i n i 1 sub i x i sub i n i sub i y i sub i n i sub i b i and i y i sub i n i 1 sub i x i sub i n i sub i y i sub i n i sub 1 where i b i ≥ 4 |
| topic | equilibrium point periodic solution system of piecewise linear difference equation |
| url | https://www.mdpi.com/2227-7390/9/12/1390 |
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