On the Solutions of Three-Dimensional System of Difference Equations via Recursive Relations of Order Two and Applications

Kara, Merve; Yazlık, Yasin

doi:10.11948/20210305

Cited by 7 publications

(3 citation statements)

References 28 publications

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“…and presented the formula for solutions as well as their asymptotic behavior. For similar studies on difference equations of this form, the reader can refer to [5][6][7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

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Dynamics and Solutions of Higher-Order Difference Equations

Folly-Gbetoula

2023

Mathematics

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The invariance method, known as Lie analysis, consists of finding a group of transformations that leave a difference equation invariant. This powerful tool permits one to lower the order, linearize and more importantly, obtain analytical solutions of difference and differential equations. In this study, we obtain the solutions and periodic solutions for some family of difference equations. We achieve this by performing an invariance analysis of this family. Eventually, symmetries are derived and used to construct canonical coordinates required for the derivation of the solutions. Moreover, periodic aspects of these solutions and the stability character of the equilibrium points are investigated.

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Section: Introductionmentioning

confidence: 99%

“…admitted by the group of transformations (7). Accordingly, the infinitesimal condition for invariance is given by η(n + 6k, x n+6 ) − X(A) = 0, that is,…”

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confidence: 99%

Dynamics and Solutions of Higher-Order Difference Equations

Folly-Gbetoula

2023

Mathematics

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“…Recently, Elsayed et al [27][28][29], Al-Basyouni and Elsayed [30], and Kara and Yazlik [31] established solutions to for certain categories of DIEs. In [27], Elsayed and Alofi studied the properties of solutions to a system of DIEs and provided solutions to this system.…”

Section: Introductionmentioning

confidence: 99%

The Dynamics of a General Model of the Nonlinear Difference Equation and Its Applications

Moaaz,

Altuwaijri

2023

Axioms

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This article investigates the qualitative properties of solutions to a general difference equation. Studying the properties of solutions to general difference equations greatly contributes to the development of theoretical methods and provides many pieces of information that may help to understand the behavior of solutions of some special models. We present the sufficient and necessary conditions for the existence of prime period-two and -three solutions. We also obtain a complete perception of the local stability of the studied equation. Then, we investigate the boundedness and global stability of the solutions. Finally, we support the validity of the results by applying them to some special cases, as well as numerically simulating the solutions.

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On a solvable four-dimensional system of difference equations

Erdem,

Yazlik

2024

Mathematica Slovaca

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In this paper we show that the following four-dimensional system of difference equations x n + 1 = y n α z n − 1 β , y n + 1 = z n γ t n − 1 δ , z n + 1 = t n ϵ x n − 1 μ , t n + 1 = x n ξ y n − 1 ρ , n ∈ N 0 , $$\begin{array}{} \displaystyle x_{n+1}=y_{n}^{\alpha}z_{n-1}^{\beta}, \quad y_{n+1}=z_{n}^{\gamma}t_{n-1}^{\delta}, \quad z_{n+1}=t_{n}^{\epsilon}x_{n-1}^{\mu}, \quad t_{n+1}=x_{n}^{\xi}y_{n-1}^{\rho}, \qquad n\in \mathbb{N}_{0}, \end{array}$$ where the parameters α, β, γ, δ, ϵ, μ, ξ, ρ ∈ ℤ and the initial values x –i , y –i , z –i , t –i , i ∈ {0, 1}, are real numbers, can be solved in closed forms, extending further some results in literature.

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On the Solutions of Three-Dimensional System of Difference Equations via Recursive Relations of Order Two and Applications

Cited by 7 publications

References 28 publications

Dynamics and Solutions of Higher-Order Difference Equations

Dynamics and Solutions of Higher-Order Difference Equations

The Dynamics of a General Model of the Nonlinear Difference Equation and Its Applications

On a solvable four-dimensional system of difference equations

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