Global behavior of P-dimensional difference equations system

Khelifa, Amira; Halim, Yacine

doi:10.3934/era.2021029

Cited by 5 publications

(2 citation statements)

References 17 publications

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“…Finally, they showed that the positive solutions of System (3) are boundedness and persistence, and that the unique positive equilibrium point of System (2) is globally asymptotically stable. Other related difference equations and systems of difference equations can be found in references [10][11][12][13][14][15][16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

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Dynamics of a Higher-Order Three-Dimensional Nonlinear System of Difference Equations

Hassani,

Yazlik,

Touafek

et al. 2023

Mathematics

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In this paper, we study the semi-cycle analysis of positive solutions and the asymptotic behavior of positive solutions of three-dimensional system of difference equations with a higher order under certain parametric conditions. Furthermore, we show the boundedness and persistence, the rate of convergence of the solutions and the global asymptotic stability of the unique equilibrium point of the proposed system under certain parametric conditions. Finally, for this system, we offer some numerical examples which support our analytical results.

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Section: Introductionmentioning

confidence: 99%

“…. , k} are arbitrary positive numbers, which was considered in [16] with p = 3. So, we suppose that X ̸ = Y ̸ = Z.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a Higher-Order Three-Dimensional Nonlinear System of Difference Equations

Hassani,

Yazlik,

Touafek

et al. 2023

Mathematics

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Stability analysis of a three-dimensional system of difference equations with quadratic terms

Yazlık,

Fidancı,

Hassani

2024

J. Appl. Math. Comput.

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This study is involved with a class of three-dimensional system of difference equations incorporating quadratic term, which naturally extends and improve several results in the literature. Firstly, we demonstrate the existence of fixed points, the boundedness, persistence and invariance of positive solution of the mentioned system. Later, for this system, we give the global asymptotic stability at fixed point and the rate of convergence result which play an important role in the discrete dynamical systems. And lastly, some numerical examples are given to validate the effectiveness and feasibility of the theoretical findings.

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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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Global behavior of P-dimensional difference equations system

Cited by 5 publications

References 17 publications

Dynamics of a Higher-Order Three-Dimensional Nonlinear System of Difference Equations

Dynamics of a Higher-Order Three-Dimensional Nonlinear System of Difference Equations

Stability analysis of a three-dimensional system of difference equations with quadratic terms

On a solvable four-dimensional system of difference equations

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