Dynamics and behavior of a higher order rational difference equation
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Authors
E. M. Elsayed
- Mathematics Department, Faculty of Science, King AbdulAziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia.
Abstract
We study the global result, boundedness, and periodicity of solutions of the difference equation
\[x_{n+1} = a +\frac{bx_{n-l} + cx_{n-k}}{dx_{n-l} + ex_{n-k}};\qquad
n = 0; 1; ... ;\]
where the parameters a; b; c; d, and e are positive real numbers and the initial conditions \(x_{-t}; x_{-t+1}; ...; x_{-1}\)
and \(x_0\) are positive real numbers where \(t = \max\{l; k\}; l \neq k\).
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ISRP Style
E. M. Elsayed, Dynamics and behavior of a higher order rational difference equation, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 4, 1463--1474
AMA Style
Elsayed E. M., Dynamics and behavior of a higher order rational difference equation. J. Nonlinear Sci. Appl. (2016); 9(4):1463--1474
Chicago/Turabian Style
Elsayed, E. M.. "Dynamics and behavior of a higher order rational difference equation." Journal of Nonlinear Sciences and Applications, 9, no. 4 (2016): 1463--1474
Keywords
- Rational difference equations
- rational systems
- periodicity.
MSC
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