Paper's Title:

Complete Analysis of Global Behavior of Certain System of Piecewise Linear Difference Equations

Author(s):

Atiratch Laoharenoo, Ratinan Boonklurb and Watcharapol Rewlirdsirikul

Department of Mathematics and Computer Science,
Kamnoetvidya Science Academy, Rayong 21210
Thailand.
E-mail: atiratch.l@kvis.ac.th

 
Department of Mathematics and Computer Science,
Faculty of Science, Chulalongkorn University, Bangkok 10330
Thailand.
E-mail: ratinan.b@chula.ac.th

Department of Mathematics and Computer Science,
Faculty of Science, Chulalongkorn University, Bangkok 10330
Thailand.
E-mail: 6570104323@student.chula.ac.th

Abstract:

Our goal 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 and b ≥ 6. We can prove that the behavior of the solution can be divided into 2 types depending on the region of initial condition (x₀,y₀). That is, the solution eventually becomes the equilibrium point. Otherwise, the solution eventually becomes the periodic solution of prime period 5. All regions of initial condition for each type of solution are determined.

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