On the global asymptotic stability of a system of difference equations with quadratic terms

In this paper, we study the qualitative behavior of the rational recursive equation \begin{equation*} x_{n+1}=\frac{x_{n-4}}{\pm1\pm x_{n}x_{n-1}x_{n-2}x_{n-3}x_{n-4}}, \quad n \in \mathbb{N}_{0}:=\{0\}\cup\mathbb N, \end{equation*} where the initial conditions are arbitrary nonzero real numbers. The main goal of this paper, is to obtain the forms of the solutions of the nonlinear fifth-order difference equations, where the initial conditions are arbitrary positive real numbers. Moreover, we investigate stability, boundedness, oscillation and the periodic character of these solutions. The results presented in this paper improve and extend some corresponding results in the literature.

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“…E. Tasdemir [17] studied the global asymptotic stability of the following system of difference equations with quadratic terms…”

Section: Introductionmentioning

confidence: 99%

Dynamical behavior of one rational fifth-order difference equation

Oğul

Şimşek

2023

Carpathian Math. Publ.

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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%

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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“…In [12], Taşdemir investigated the oscillation, global asymptotic stability and rate of convergence of solutions of following system of second order difference equations with quadratic terms…”

Section: Introductionmentioning

confidence: 99%