On the behavior of solutions of the system of rational difference equations x n + 1 = x n - 1 y n x n - 1 - 1 , y n + 1 = y n - 1 x n y n - 1 - 1 , z n + 1 = 1 y n z n

Kurbanlı, Abdullah Selçuk

doi:10.1186/1687-1847-2011-40

Cited by 21 publications

(15 citation statements)

References 26 publications

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“…Then, f(x n ; y n ; z n )g Proof. Assume that (14) holds. (The case where (15) holds is similar and will be omitted.)…”

Section: Oscillation Behavior and Existence Of Unbounded Solutionsmentioning

confidence: 99%

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Global behavior of a three-dimensional system of difference equations of order three

Tollu¹,

Yalçınkaya²

2018

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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In this paper, we investigate the global behavior of the positive solutions of the system of di¤erence equations u n+1 = 1 u n 1 1 + 1 v p n 2 ; v n+1 = 2 v n 1 2 + 2 w q n 2 ; w n+1 = 3 w n 1 3 + 3 u r n 2 for n 2 N 0 where the initial conditions u i ; v i ; w i (i = 0; 1; 2) are nonnegative real numbers and the parameters j ; j ; j (j = 1; 2; 3) and p; q; r are positive real numbers, by extending some results in the literature.

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“…Then, f(x n ; y n ; z n )g Proof. Assume that (14) holds. (The case where (15) holds is similar and will be omitted.)…”

Section: Oscillation Behavior and Existence Of Unbounded Solutionsmentioning

confidence: 99%

“…where the initial conditions x 1 , x 0 , y 1 , y 0 , z 1 , z 0 are real numbers. See also [13,14,16]. Yazlik et al [34] obtained the explicit solutions of a three-dimensional system of di¤erence equations with multiplicative terms…”

Section: Introductionmentioning

confidence: 99%

Global behavior of a three-dimensional system of difference equations of order three

Tollu¹,

Yalçınkaya²

2018

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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“…Many papers deal with the difference equations system. We refer in particular to [11][12][13][14] where further references can be found.…”

Section: Introductionmentioning

confidence: 99%

Explicit Solutions and Bifurcations for a System of Rational Difference Equations

2019

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In this paper, we consider the explicit solution of the following system of nonlinear rational difference equations: x n + 1 = x n - 1 / x n - 1 + r , y n + 1 = x n - 1 y n / x n - 1 y n + r , with initial conditions x - 1 , x 0 and y 0 , which are arbitrary positive real numbers. By doing this, we encounter the hypergeometric function. We also investigate global dynamics of this system. The global dynamics of this system consists of two kind of bifurcations.

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“…In the same year, Kurbanli [22] studied the behavior of the solutions of the system of rational difference equations…”

Section: Introductionmentioning

confidence: 99%

On the solutions and periodicity of some nonlinear systems of difference equations

El-Dessoky¹

2016

J. Nonlinear Sci. Appl.

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On the behavior of solutions of the system of rational difference equations x n + 1 = x n - 1 y n x n - 1 - 1 , y n + 1 = y n - 1 x n y n - 1 - 1 , z n + 1 = 1 y n z n

Abstract: In this article, we investigate the solutions of the system of difference equationsnumbers such that y 0 x -1 ≠ 1, x 0 y -1 ≠ 1 and y 0 z 0 ≠ 0.

Cited by 21 publications

References 26 publications

Global behavior of a three-dimensional system of difference equations of order three

Global behavior of a three-dimensional system of difference equations of order three

Explicit Solutions and Bifurcations for a System of Rational Difference Equations

On the solutions and periodicity of some nonlinear systems of difference equations

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