Dynamics of the nonlinear rational difference equation $x_{n+1} = Ax_n + Bx_{n−k} + frac{px_n+x_{n−k}}{q+x_{n−k}}$

ZAYED, E. M. E.

Dynamics of the nonlinear rational difference equation $x_{n+1} = Ax_n + Bx_{n−k} + frac{px_n+x_{n−k}}{q+x_{n−k}}$

E. M. E. ZAYED (Mathematics Department, Faculty of Science, Taif Univercity El Taif, EL Hawiyah, Kingdom of Saudi, Arabia)

European Journal of Pure and Applied Mathematics (elektronik)

4 0

Yıl: 2010 Cilt: 3 Sayı: 2 Sayfa Aralığı: 0 - 0 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

Dynamics of the nonlinear rational difference equation $x_{n+1} = Ax_n + Bx_{n−k} + frac{px_n+x_{n−k}}{q+x_{n−k}}$

Öz:

In this article, we study the global stability and the asymptotic properties of the nonnegative solutions of the nonlinear difference equation $x_{n+1} = Ax_n + Bx_{n−k} + frac{px_n+x_{n−k}}{q+x_{n−k}}$, n = 0,1,2, ..... where the parameters A, B, p, q and the initial conditions $x_{−k},...,x_{−1}, x_0$ are arbitrary nonnegative real numbers, while k is a positive integer number. Some numerical examples will be given to illustrate our results. 2000 Mathematics Subject Classifications: 39A10,39A11,39A99,34C99

Anahtar Kelime:

Konular: Matematik

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

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APA	ZAYED E (2010). Dynamics of the nonlinear rational difference equation $x_{n+1} = Ax_n + Bx_{n−k} + frac{px_n+x_{n−k}}{q+x_{n−k}}$. , 0 - 0.
Chicago	ZAYED E. M. E. Dynamics of the nonlinear rational difference equation $x_{n+1} = Ax_n + Bx_{n−k} + frac{px_n+x_{n−k}}{q+x_{n−k}}$. (2010): 0 - 0.
MLA	ZAYED E. M. E. Dynamics of the nonlinear rational difference equation $x_{n+1} = Ax_n + Bx_{n−k} + frac{px_n+x_{n−k}}{q+x_{n−k}}$. , 2010, ss.0 - 0.
AMA	ZAYED E Dynamics of the nonlinear rational difference equation $x_{n+1} = Ax_n + Bx_{n−k} + frac{px_n+x_{n−k}}{q+x_{n−k}}$. . 2010; 0 - 0.
Vancouver	ZAYED E Dynamics of the nonlinear rational difference equation $x_{n+1} = Ax_n + Bx_{n−k} + frac{px_n+x_{n−k}}{q+x_{n−k}}$. . 2010; 0 - 0.
IEEE	ZAYED E "Dynamics of the nonlinear rational difference equation $x_{n+1} = Ax_n + Bx_{n−k} + frac{px_n+x_{n−k}}{q+x_{n−k}}$." , ss.0 - 0, 2010.
ISNAD	ZAYED, E. M. E.. "Dynamics of the nonlinear rational difference equation $x_{n+1} = Ax_n + Bx_{n−k} + frac{px_n+x_{n−k}}{q+x_{n−k}}$". (2010), 0-0.

APA	ZAYED E (2010). Dynamics of the nonlinear rational difference equation $x_{n+1} = Ax_n + Bx_{n−k} + frac{px_n+x_{n−k}}{q+x_{n−k}}$. European Journal of Pure and Applied Mathematics (elektronik), 3(2), 0 - 0.
Chicago	ZAYED E. M. E. Dynamics of the nonlinear rational difference equation $x_{n+1} = Ax_n + Bx_{n−k} + frac{px_n+x_{n−k}}{q+x_{n−k}}$. European Journal of Pure and Applied Mathematics (elektronik) 3, no.2 (2010): 0 - 0.
MLA	ZAYED E. M. E. Dynamics of the nonlinear rational difference equation $x_{n+1} = Ax_n + Bx_{n−k} + frac{px_n+x_{n−k}}{q+x_{n−k}}$. European Journal of Pure and Applied Mathematics (elektronik), vol.3, no.2, 2010, ss.0 - 0.
AMA	ZAYED E Dynamics of the nonlinear rational difference equation $x_{n+1} = Ax_n + Bx_{n−k} + frac{px_n+x_{n−k}}{q+x_{n−k}}$. European Journal of Pure and Applied Mathematics (elektronik). 2010; 3(2): 0 - 0.
Vancouver	ZAYED E Dynamics of the nonlinear rational difference equation $x_{n+1} = Ax_n + Bx_{n−k} + frac{px_n+x_{n−k}}{q+x_{n−k}}$. European Journal of Pure and Applied Mathematics (elektronik). 2010; 3(2): 0 - 0.
IEEE	ZAYED E "Dynamics of the nonlinear rational difference equation $x_{n+1} = Ax_n + Bx_{n−k} + frac{px_n+x_{n−k}}{q+x_{n−k}}$." European Journal of Pure and Applied Mathematics (elektronik), 3, ss.0 - 0, 2010.
ISNAD	ZAYED, E. M. E.. "Dynamics of the nonlinear rational difference equation $x_{n+1} = Ax_n + Bx_{n−k} + frac{px_n+x_{n−k}}{q+x_{n−k}}$". European Journal of Pure and Applied Mathematics (elektronik) 3/2 (2010), 0-0.