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

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

References

1. [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. [2] F. Bozkurt, Stability analysis of nonlinear difference equation, International Journal of Modern Nonlinear Theory and Application, 2 (1) (2013), 1-6.
3. [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. [4] R. Karatas, C. Cinar and D. Simsek, On the positive solutions of the Difference equation xn+1 = xn
5. [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. [6] Q. Din, M. N. Qureshi and A. Q. Khan, Dynamic of Fourth- order system of rational difference equations, 2012 (2012): 215.