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Explicit Solutions and Bifurcations for a System of Rational Difference Equations

Author

Listed:
  • Bashir Al-Hdaibat

    (Department of Mathematics, Hashemite University, P.O. Box 330127, Zarqa 13133, Jordan)

  • Saleem Al-Ashhab

    (Department of Mathematics, Al-albayt University, Mafraq 25113, Jordan)

  • Ramadan Sabra

    (Department of Mathematics, Jazan University, Jazan 45142, Saudi Arabia)

Abstract

In this paper, we consider the explicit solution of the following system of nonlinear rational difference equations: x n + 1 = x n − 1 / x n − 1 + r , y n + 1 = x n − 1 y n / x n − 1 y n + r , with initial conditions x − 1 , x 0 and y 0 , which are arbitrary positive real numbers. By doing this, we encounter the hypergeometric function. We also investigate global dynamics of this system. The global dynamics of this system consists of two kind of bifurcations.

Suggested Citation

  • Bashir Al-Hdaibat & Saleem Al-Ashhab & Ramadan Sabra, 2019. "Explicit Solutions and Bifurcations for a System of Rational Difference Equations," Mathematics, MDPI, vol. 7(1), pages 1-9, January.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:1:p:69-:d:196294
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    References listed on IDEAS

    as
    1. Piet H. Pellenbarg & Paul J.M. Van Steen, 2008. "The Netherlands in Maps," Tijdschrift voor Economische en Sociale Geografie, Royal Dutch Geographical Society KNAG, vol. 99(3), pages 374-374, July.
    2. Piet H. Pellenbarg & Paul J.M. Van Steen, 2008. "The Netherlands in Maps," Tijdschrift voor Economische en Sociale Geografie, Royal Dutch Geographical Society KNAG, vol. 99(2), pages 266-266, April.
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