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# Global and Local Behavior of the System of Piecewise Linear Difference Equations xn+1 = |xn| − yn − b and yn+1 = xn − |yn| + 1 Where b ≥ 4

by 2,* and
1
The Demonstration School of Silpakorn University, Faculty of Education, Silpakorn University, Nakhon Pathom 73000, Thailand
2
Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand
*
Author to whom correspondence should be addressed.
Academic Editors: Christopher Goodrich, Diana Savin, Nicusor Minculete and Vincenzo Acciaro
Mathematics 2021, 9(12), 1390; https://doi.org/10.3390/math9121390
Received: 14 May 2021 / Revised: 2 June 2021 / Accepted: 11 June 2021 / Published: 15 June 2021
The aim of this article is to study the system of piecewise linear difference equations ${x}_{n+1}=|{x}_{n}|-{y}_{n}-b$ and ${y}_{n+1}={x}_{n}-|{y}_{n}|+1$ where $n\ge 0$. A global behavior for $b=4$ shows that all solutions become the equilibrium point. For a large value of $|{x}_{0}|$ and $|{y}_{0}|$, we can prove that (i) if $b=5$, then the solution becomes the equilibrium point and (ii) if $b\ge 6$, then the solution becomes the periodic solution of prime period 5. View Full-Text
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MDPI and ACS Style

Aiewcharoen, B.; Boonklurb, R.; Konglawan, N. Global and Local Behavior of the System of Piecewise Linear Difference Equations xn+1 = |xn| − ynb and yn+1 = xn − |yn| + 1 Where b ≥ 4. Mathematics 2021, 9, 1390. https://doi.org/10.3390/math9121390

AMA Style

Aiewcharoen B, Boonklurb R, Konglawan N. Global and Local Behavior of the System of Piecewise Linear Difference Equations xn+1 = |xn| − ynb and yn+1 = xn − |yn| + 1 Where b ≥ 4. Mathematics. 2021; 9(12):1390. https://doi.org/10.3390/math9121390

Chicago/Turabian Style

Aiewcharoen, Busakorn, Ratinan Boonklurb, and Nanthiya Konglawan. 2021. "Global and Local Behavior of the System of Piecewise Linear Difference Equations xn+1 = |xn| − ynb and yn+1 = xn − |yn| + 1 Where b ≥ 4" Mathematics 9, no. 12: 1390. https://doi.org/10.3390/math9121390

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