AN INVESTIGATION OF THE SOLUTIONS AND THE DYNAMIC BEHAVIOR OF SOME RATIONAL DIFFERENCE EQUATIONS

Year 2023, Volume: 6 Issue: 1, 55 - 80, 31.01.2023

Nisreen Bukhary

https://doi.org/10.33773/jum.1136294

Cited By: 1

https://izlik.org/JA72LB98KX

Abstract

The main purpose of this work is to investigate the solutions, the periodic character and study the global asymptotic behavior of this so- lutions of the following rational di↵erence equation
x_(n+1) = x_(n-2)*x_(n-6) / x_(n-3)*(±1 ± x_(n-2)*x_(n-6))
with a non-zero real numbers initial conditions.

Keywords

Di↵erence Equation , Recursive sequences , Stability , Periodi

Supporting Institution

King Abdulaziz universitylaziz

References

• [1] R. Abo-Zeid, On the Solutions of a Fourth Order Difference Equation, Universal Journal of Mathematics and Applications, 4 (2) (2021), 76-81.
• [2] F. Bozkurt, Stability analysis of nonlinear difference equation, International Journal of Modern Nonlinear Theory and Application, 2 (1) (2013), 1-6.
• [3] D. S. Dilip and S. M. Mathew, Dynamic of a second order nonlinear difference system with exponents, Journal of the Egyptian Mathematical Society, 29 (1) (2021), 1-10.
• [4] R. Karatas, C. Cinar and D. Simsek, On the positive solutions of the Difference equation xn+1 = xn
• [5] E. M. Elsayed and M. M. El-dessoky, Dynamics and global behavior for a fourth order rational difference equation, Hacettepe Journal of Mathematics and Statistics, 42 (5) (2013), 479-494.
• [6] Q. Din, M. N. Qureshi and A. Q. Khan, Dynamic of Fourth- order system of rational difference equations, 2012 (2012): 215.