Investigating dynamical behaviors of the difference equation \(x_{n+1}= \frac{Cx_{n-5}}{A+Bx_{n-2}x_{n-5}}\)

Ghazel, M.; Elsayed, E. M.; Matouk, A. E.; Mousallam, A. M.

doi:10.22436/jnsa.010.09.09

Cited by 7 publications

(3 citation statements)

References 30 publications

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“…1, yields the second order difference equation that was considered in Cinar (2004b). On the other hand, substituting = 3 and replacing and by / and / respectively produce the sixth order difference equation considered in Ghazel et al (2017).…”

Section: Introduction *Mathematicsmentioning

confidence: 99%

Dynamical study of the class of difference equation Xn+1= Xn-2q+1/A+BXn-2qXn-q+1

Ghazel¹

2020

Int. j. adv. appl. sci.

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This work is devoted to present a study of the class of the difference equations x n+1 = x n−2q+1 A + Bx n−2q+1 x n−q+1 , q = 1,2, … ⁄ with arbitrary initial data, where and are arbitrary parameters, and is an arbitrary nonnegative integer. We present a detailed investigation of the behavior of the solution, including their dependence on parameters and initial conditions. Local and global stabilities of the equilibrium points are discussed. The existence of a periodic solution is studied. Numerical simulations are given to assure the correctness of the analytical results. This study improves and surpasses studies of several forms of difference equations that have been investigated earlier by many researchers.

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Section: Introduction *Mathematicsmentioning

confidence: 99%

Dynamical study of the class of difference equation Xn+1= Xn-2q+1/A+BXn-2qXn-q+1

Ghazel¹

2020

Int. j. adv. appl. sci.

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“…In [5], the authors concerned with presenting the qualitative behaviour of the sixth order difference equation…”

Section: Introductionmentioning

confidence: 99%

Analysis of the Convergence and Periodicity of a Rational Difference Equation

Almatrafi¹,

Alzubaidi²

2019

Journal of Mathematical Sciences and Modelling

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The exact solutions of most difference equations cannot be obtained sometimes. This can be attributed to the fact that there is no a specific approach from which one can find the exact solution. Therefore, many researchers tend to study the qualitative behaviours of these equations. In this paper, we will investigate some qualitative properties such as local stability, global stability, periodicity and solutions of the following eighth order recursive equation x n+1 = c 1 x n−3 − c 2 x n−3 c 3 x n−3 − c 4 x n−7 , n = 0, 1, ..., where the coefficients c i , for all i = 1, ..., 4, are assumed to be positive real numbers and the initial conditions x i for all i = −7, −6, ..., 0, are arbitrary non-zero real numbers.

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“…In [5], the authors concerned with showing an analytical investigation about the following sixth-order difference equation…”

Section: Introductionmentioning

confidence: 99%

Untitled

2019

Open J. Discret. Appl. Math.

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The exact solutions of most nonlinear difference equations cannot be obtained theoretically sometimes. Therefore, a massive number of researchers predict the long behaviour of most difference equations by investigating some qualitative behaviours of these equations from the governing equations. In this article, we aim to analyze the asymptotic stability, global stability, periodicity of the solution of an eighth-order difference equation. Moreover, a theoretical solution of a special case equation will be presented in this paper.

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Investigating dynamical behaviors of the difference equation \(x_{n+1}= \frac{Cx_{n-5}}{A+Bx_{n-2}x_{n-5}}\)

Cited by 7 publications

References 30 publications

Dynamical study of the class of difference equation Xn+1= Xn-2q+1/A+BXn-2qXn-q+1

Dynamical study of the class of difference equation Xn+1= Xn-2q+1/A+BXn-2qXn-q+1

Analysis of the Convergence and Periodicity of a Rational Difference Equation

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