Explicit Solutions and Bifurcations for a System of Rational Difference Equations

Bashir Al-Hdaibat, Saleem Al-Ashhab and Ramadan Sabra
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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

Mathematics, 2019, vol. 7, issue 1, 1-9

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.

Keywords: difference equation; hypergeometric function; bifurcation; MatContM (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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