Dynamical behavior of rational difference equation $x_{n+1}=\dfrac{x_{n-13}}{\pm1\pm x_{n-1}x_{n-3}x_{n-5}x_{n-7}x_{n-9} x_{n-11}x_{n-13}}$

D. Şimşek; B. Oğul; F. G. Abdullayev

doi:10.3842/umzh.v76i7.7548

D. Şimşek Konya Technical University, Turkey
B. Oğul Istanbul Aydin University, Turkey
F. G. Abdullayev Mersin University, Turkey and Kyrgyz–Turkish Manas University, Bishkek, Kyrgyz Republic

DOI: https://doi.org/10.3842/umzh.v76i7.7548

Keywords: Local stability, Periodic solution, Dierence equation.

Abstract

UDC 517.9

Discrete-time systems are sometimes used to explain natural phenomena encountered in nonlinear sciences. We study the periodicity, boundedness, oscillation, stability, and some exact solutions of nonlinear difference equations. Exact solutions are obtained by using the standard iteration method. Some well-known theorems are used to test the stability of the equilibrium points. Some numerical examples are also provided to confirm the validity of the theoretical results. The numerical component is implemented with the Wolfram Mathematica. The presented method may be simply applied to other rational recursive issues.

In this paper, we explore the dynamics of adhering to rational difference formula \begin{equation*}x_{n+1}=\frac{x_{n-13}}{\pm1\pm x_{n-1}x_{n-3}x_{n-5}x_{n-7}x_{n-9} x_{n-11}x_{n-13}},\end{equation*} where the initials are arbitrary nonzero real numbers.

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