Global and Local Behavior of 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 b ? 4

Busakorn Aiewcharoen, Ratinan Boonklurb and Nanthiya Konglawan
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Busakorn Aiewcharoen: The Demonstration School of Silpakorn University, Faculty of Education, Silpakorn University, Nakhon Pathom 73000, Thailand
Ratinan Boonklurb: Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand
Nanthiya Konglawan: Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand

Mathematics, 2021, vol. 9, issue 12, 1-27

Abstract: 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 ? 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 ? 6 , then the solution becomes the periodic solution of prime period 5.

Keywords: equilibrium point; periodic solution; system of piecewise linear difference equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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