On the global behavior of 𝑥ᵤ₊₁ = |𝑥ᵤ|− 𝑦ᵤ − 1 and 𝑦ᵤ₊₁ = 𝑥ᵤ +|𝑦ᵤ|

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DOI:

https://doi.org/10.4067/S0719-06462012000200007

Abstract

In this paper we consider the system of piecewise linear difference equations in the title, where the initial conditions x0 and y0 are real numbers. We show that there exists a unique equilibrium solution and exactly two prime period-3 solutions, and that except for the unique equilibrium solution, every solution of the system is eventually one of the two prime period-3 solutions.

Keywords

Periodic solution , systems of piecewise linear difference equations
  • E. A. Grove Department of Mathematics, University of Rhode Island, Kingston, Rhode Island, 02881-0816, USA.
  • E. Lapierre Department of Mathematics, Johnson and Wales University, Providence, Rhode Island 02903, USA.
  • W. Tikjha Faculty of Science and Technology, Pibulsongkram Rajabhat University, Muang District, Phitsanuloke, 65000, Thailand.
  • Pages: 111–152
  • Date Published: 2012-06-01
  • Vol. 14 No. 2 (2012): CUBO, A Mathematical Journal

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Published

2012-06-01

How to Cite

[1]
E. A. Grove, E. Lapierre, and W. Tikjha, “On the global behavior of 𝑥ᵤ₊₁ = |𝑥ᵤ|− 𝑦ᵤ − 1 and 𝑦ᵤ₊₁ = 𝑥ᵤ +|𝑦ᵤ|”, CUBO, vol. 14, no. 2, pp. 111–152, Jun. 2012.

Issue

Vol. 14 No. 2 (2012): CUBO, A Mathematical Journal

Section

Articles