TITLE:
The Solutions and the Dynamic Behavior of the Rational Difference Equations
AUTHORS:
Nisreen A. Bukhary, Elsayed M. Elsayed
KEYWORDS:
Difference Equation, Local Stability, Global Attractor, Boundedness, Periodic
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.11 No.2,
February
22,
2023
ABSTRACT: The main purpose of this paper is to study the dynamic behavior of the rational difference equation of the fourth order
Where α, β and γ are positive constants and the initial conditions y-3, y-2, y-1, y0 are arbitrary positive real numbers. Also, we obtain the solution of some special cases of this equation and investigate the existence of a periodic solutions of these equations. Finally, some numerical examples will be given to explicate our results.