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

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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Bibliographic Details
Main Authors: Busakorn Aiewcharoen, Ratinan Boonklurb, Nanthiya Konglawan
Format: Article
Language:English
Published: MDPI AG 2021-06-01
Series:Mathematics
Subjects:
equilibrium point
periodic solution
system of piecewise linear difference equation
Online Access:https://www.mdpi.com/2227-7390/9/12/1390
Description
Summary: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.
ISSN:2227-7390

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