On the global behavior of

• E.A Grove ^[1] ; E Lapierre ^[2] ; W Tikjha ^[3]
  1. [1] University of Rhode Island

     University of Rhode Island

     Town of South Kingstown, Estados Unidos

     
  2. [2] Johnson and Wales University Department of Mathematics
  3. [3] Pihulsongkram Rajabhat University Faculty of Science and Technology

  Mostrar afiliaciones +
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 14, Nº. 2, 2012, págs. 111-152
• Idioma: inglés
• DOI: 10.4067/S0719-06462012000200007
• Enlaces
  • Texto completo
• Resumen
  • español

    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.

  • English

    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.

• Referencias bibliográficas
  • Camouzis, E,Ladas, G. (2008). Dynamics of Third-Order Rational Difference Equations with Open Problems and Conjectures. Chapman & Hall/CRC....
  • Devaney, R.L. (1984). A piecewise linear model of the the zones of instability of an area-preserving map. Physica. 10. 387-393
  • Kulenovic, M.R.S,Merino, O. (2002). Discrete Dynamical Systems and Difference Equations with Mathematica. Chapman & Hall/CRC. New York.
  • Peitgen, H.O,Saupe, D. (1991). The Science of Fractal Images. Springer-Verlog. New York.
  • Tikjha, W,Lenbury, Y,Lapierre, E. G. (2010). On the Global Character of the System of Piecewise Linear Difference Equations. Advances in Difference...