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Cubo (Temuco)

versión On-line ISSN 0719-0646

Cubo vol.14 no.2 Temuco  2012 

CUBO A Mathematical Journal Vol.14, No'02, (111-152). June 2012

Texto completo disponíble en formato PDF

On the global behavior of


E.A. Grove*, E. Lapierre** and W. Tikjha***

*Department of Mathematics, University of Rhode Island, Kingston, Rhode Island, 02881-0816, USA email:

**Department ofMathematics, Johnson and Wales University, Providence, Rhode Island02903, USA. email:

***Faculty ofScience andTechnology, Pihulsongkram Rajabhat University, Muang District, Phitsanuloke,65000, Thailand email:


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 and Phrases: Periodic solution; systems of piecewise linear difference equations 2010 AMS Mathematics Subject Classification: 39A10, 65Q10.


En este artículo consideramos el sistema de ecuaciones en diferencia lineales por partes indicado en el título, donde las condiciones iniciales x0 e y0 son números reales. Demostramos que existe una única solución de equilibrio y exactamente dos soluciones de período 3-primo, y que exceptuando la soluciún única de equilibrio, toda solucion del sistema es eventualmente una de las dos soluciones de periodo 3-primo.


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[5] W. Tikjha, Y. Lenbury, and E. G. Lapierre, On the Global Character of the System of Piecewise Linear Difference Equations , Advances in Difference Equations, ,Volume 2010 (2010), Article ID 573281.         [ Links ]

Received:November 2011.Revised:November 2011.

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