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Cubo (Temuco)

versión On-line ISSN 0719-0646

Cubo vol.14 no.2 Temuco  2012

http://dx.doi.org/10.4067/S0719-06462012000200007 

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: grove@math.uri.edu

**Department ofMathematics, Johnson and Wales University, Providence, Rhode Island02903, USA. email: elapierre@jwu.edu

***Faculty ofScience andTechnology, Pihulsongkram Rajabhat University, Muang District, Phitsanuloke,65000, Thailand email: wirot_tik@yahoo.com


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


RESUMEN

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.


References

[1] E. Camouzis, and G. Ladas, Dynamics of Third-Order Rational Difference Equations with Open Problems and Conjectures, Chapman & Hall/CRC, New York, 2008.         [ Links ]

[2] R.L. Devaney, A piecewise linear model of the the zones of instability of an area-preserving map, Physica 10D (1984), 387-393.         [ Links ]

[3] M.R.S. Kulenovic, and O. Merino, Discrete Dynamical Systems and Difference Equations with Mathematica, Chapman & Hall/CRC, New York, 2002.         [ Links ]

[4] H.O. Peitgen and D. Saupe, (eds.) The Science of Fractal Images, Springer-Verlog, New York,1991.         [ Links ]

[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.