Dynamics and behavior of a higher order rational difference equation

Elsayed, E. M.¹

¹ Mathematics Department, Faculty of Science, King AbdulAziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia

Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 4, p. 1463-1474.

Résumé

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 $t = \max\{l; k\}; l \neq k$.

Détail

DOI : 10.22436/jnsa.009.04.06

Classification : 39A10, 39A11, 39A20
Keywords: Rational difference equations, rational systems, periodicity.

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