Dynamical behavior of rational difference equation $$x_{n+1}=\frac{x_{n-17}}{\pm 1\pm x_{n-2}x_{n-5}x_{n-8}x_{n-11}x_{n-14}x_{n-17}}$$

Oğul, Burak; Şimşek, Dağıstan; Öğünmez, Hasan; Kurbanlı, Abdullah Selçuk

doi:10.1007/s40590-021-00357-9

Bol. Soc. Mat. Mex.

2021

DOI: 10.1007/s40590-021-00357-9

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Dynamical behavior of rational difference equation $$x_{n+1}=\frac{x_{n-17}}{\pm 1\pm x_{n-2}x_{n-5}x_{n-8}x_{n-11}x_{n-14}x_{n-17}}$$

Burak Oğul

Dağıstan Şimşek

Hasan Öğünmez

et al.

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Cited by 4 publications

References 26 publications

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Dynamical Analysis and Solutions of Nonlinear Difference Equations of Thirty Order

Oğul,

Şimşek

2024

Universal Journal of Mathematics and Applications

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Discrete-time systems are sometimes used to explain natural phenomena that happen in nonlinear sciences. We study the periodicity, boundedness, oscillation, stability, and certain exact solutions of nonlinear difference equations in this paper. Using the standard iteration method, exact solutions are obtained. Some well-known theorems are used to test the stability of the equilibrium points. Some numerical examples are also provided to confirm the theoretical work’s validity. The numerical component is implemented with Wolfram Mathematica. The method presented may be simply applied to other rational recursive issues. \par In this paper, we explore the dynamics of adhering to rational difference formula \begin{equation*} x_{n+1}=\frac{x_{n-29}}{\pm1\pm x_{n-5}x_{n-11}x_{n-17}x_{n-23}x_{n-29}}, \end{equation*} where the initials are arbitrary nonzero real numbers.

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Dynamical Analysis and Solutions of Nonlinear Difference Equations of Thirty Order

Oğul,

Şimşek

2024

Universal Journal of Mathematics and Applications

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A Qualitative Investigation of the Solution of the Difference Equation $\Psi_{m+1}=\frac{\Psi_{m-3}\Psi_{m-5}}{\Psi_{m-1} \left( \pm1\pm \Psi_{m-3}\Psi_{m-5} \right) }$

Oğul

Şimşek

Ibrahim

2023

Communications in Advanced Mathematical Sciences

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We explore the dynamics of adhering to rational difference formula $$\Psi_{m+1}=\frac{\Psi_{m-3}\Psi_{m-5}}{\Psi_{m-1} \left( \pm1\pm \Psi_{m-3}\Psi_{m-5} \right) } \quad m \in \mathbb{N}_{0}$$ where the initials $\Psi_{-5}$, $\Psi_{-4}$, $\Psi_{-3}$,$\Psi_{-2}$, $\Psi_{-1}$, $\Psi_{0}$ are arbitrary nonzero real numbers. Specifically, we examine global asymptotically stability. We also give examples and solution diagrams for certain particular instances.

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Dynamical behavior of rational difference equation x n + 1 = x n - 13
Şimşek,
Oğul,
Abdullayev
2024
Ukr. Mat. Zhurn.
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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 x n + 1 = x n - 13 ± 1 ± x n - 1 x n - 3 x n - 5 x n - 7 x n - 9 x n - 11 x n - 13 , where the initials are arbitrary nonzero real numbers.

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Dynamical behavior of rational difference equation $$x_{n+1}=\frac{x_{n-17}}{\pm 1\pm x_{n-2}x_{n-5}x_{n-8}x_{n-11}x_{n-14}x_{n-17}}$$

Cited by 4 publications

References 26 publications

Dynamical Analysis and Solutions of Nonlinear Difference Equations of Thirty Order

Dynamical Analysis and Solutions of Nonlinear Difference Equations of Thirty Order

A Qualitative Investigation of the Solution of the Difference Equation $\Psi_{m+1}=\frac{\Psi_{m-3}\Psi_{m-5}}{\Psi_{m-1} \left( \pm1\pm \Psi_{m-3}\Psi_{m-5} \right) }$

Dynamical behavior of rational difference equation x n + 1 = x n - 13
Şimşek,
Oğul,
Abdullayev
2024
Ukr. Mat. Zhurn.
0
0
0
0
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Dynamical behavior of rational difference equation $$x_{n+1}=\frac{x_{n-17}}{\pm 1\pm x_{n-2}x_{n-5}x_{n-8}x_{n-11}x_{n-14}x_{n-17}}$$

Cited by 4 publications

References 26 publications

Dynamical Analysis and Solutions of Nonlinear Difference Equations of Thirty Order

Dynamical Analysis and Solutions of Nonlinear Difference Equations of Thirty Order

A Qualitative Investigation of the Solution of the Difference Equation $\Psi_{m+1}=\frac{\Psi_{m-3}\Psi_{m-5}}{\Psi_{m-1} \left( \pm1\pm \Psi_{m-3}\Psi_{m-5} \right) }$

Dynamical behavior of rational difference equation x n + 1 = x n - 13 Şimşek, Oğul, Abdullayev 2024Ukr. Mat. Zhurn.0000View full textAdd to dashboardCite

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Dynamical behavior of rational difference equation x n + 1 = x n - 13
Şimşek,
Oğul,
Abdullayev
2024
Ukr. Mat. Zhurn.
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0
0
View full text Add to dashboard Cite