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  • Corpus ID: 124018376
ON STUDY OF THE ASYMPTOTIC BEHAVIOR OF SOME RATIONAL DIFFERENCE EQUATIONS@inproceedings{ElMoneam2014ONSO, title={ON STUDY OF THE ASYMPTOTIC BEHAVIOR OF SOME RATIONAL DIFFERENCE EQUATIONS}, author={Mohamed Abd El-Moneam and S. O. Alamoudy}, year={2014}, url={https://api.semanticscholar.org/CorpusID:124018376} }
  • M. A. El-MoneamS. O. Alamoudy
  • Published 2014
  • Mathematics
In this article, we study the periodicity, the boundedness and the global stability of the positive solutions of the following nonlinear difference equation xn+1 = axn + bxn−1 + cxn−2 + fxn−3 + rxn−4 dxn−1 + exn−2 + gxn−3 + sxn−4 ; n = 0; 1; 2;::::: where the coefficients a;b;c;d;e;f;g;r;s ∈ (0; ∞); while the initial conditions x−4,x−3,x−2, x−1;x0 are arbitrary positive real numbers. Some numerical examples will be given to il- lustrate our results. online.watsci.orgSave to LibrarySaveCreate AlertAlertCiteShare17 CitationsBackground Citations3View All

17 Citations

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On the Dynamics of the Solutions of the Rational Recursive Sequences

    M. A. El-MoneamMathematics
  • 2015
In this article, we study the periodicity, the boundedness and the global stability of the positive solutions of the following nonlinear difference equation xn+1 = Axn +Bxn−k + Cxn−l +Dxn−σ +… Expand
  • 10
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Global attractivity of a rational difference equation of order ten

    A. KhaliqF. AlzahraniE. ElsayedMathematics
  • 2016
In this paper, we study qualitative properties and periodic nature of the solutions of the difference equation xn+1 = axn−4 + bxn−4 cxn−4 + dxn−9 , n = 0, 1, .., where the initial conditions x−9,… Expand
  • 8
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Stability of a fractional difference equation of high order

    M. A. El-MoneamT. F. IbrahimS. ElamodyMathematicsJournal of Nonlinear Sciences and Applications
  • 2018
In this paper we investigate the local stability, global stability, and boundedness of solutions of the recursive sequence xn+1 = xn−p ( 2 xn−q + a xn−r xn−q + a xn−r ) , where x−q+k 6= −a x−r+k for… Expand
  • 22
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On the dynamics of the nonlinear rational difference equation xn+1 = Axn + Bxn−k + Cxn−l + bxn−k/dxn−k − exn−l

    M. A. El-MoneamE. ZayedMathematics
  • 2015
  • 8
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Dynamics and Global Stability of Second Order Nonlinear Difference Equation

    E. ElsayedH. S. GafelMathematicsPan-American Journal of Mathematics
  • 2022
In this paper, we study some qualitative behavior of the solutions of the following rational difference equation with order twoxn+1=axn+bxn−1+cxn+dxn−1/e+fxn−1,where the parameters a, b, c, d, e and… Expand
  • 1
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Global attractivity of a rational difference equation of order twenty

    Stephen SadiqM. KalimMathematics
  • 2018
γzn−9+δzn−19 , n = 0,1,2, . .. has been studied where the initial conditions z−19, z−18, ... , z0 are arbitrary positive real numbers and α, β, γ, δ are constants. Solutions of some special cases of… Expand
  • 4
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SOLVING A CLASS OF THREE-ORDER MAX-TYPE DIFFERENCE EQUATIONS

    T. F. IbrahimS. ArabiaMathematics
  • 2014
In this paper we will investigate the closed form solution of a class of max-type difference equation in the form xn+1 = max{ A xk ;x k 2}; n ∈ N0 where k ≥ 1, A ≥ 1 and the initial conditions x 2;x… Expand
  • 12
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Dynamics of the Rational Difference Equation

    M. A. El-MoneamE. ZayedMathematics
  • 2014
In this article, we study the periodicity, the boundedness and the global stab ility of the positive solutions of the following nonlinear difference equation
  • 125
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On the Dynamics of the Higher Order Nonlinear Rational Difference Equation

    M. A. El-MoneamMathematics
  • 2014
In this article, we study the periodicity, the boundedness and the global stab ility of the positive solutions of the following nonlinear difference equation
  • 24
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Analytical and Solutions of Fourth Order Difference Equations

    M. M. AlzubaidiE. ElsayedMathematicsCommunications in Advanced Mathematical Sciences
  • 2019
In this article, we presented the solutions of the following recursive sequences\[ x_{n+1}=\frac{x_{n-2}x_{n-3}}{x_{n}(\pm1\pm x_{n-2}x_{n-3})}, \] where the initial conditions $x_{-3}\ ,x_{-2}\… Expand
  • 4
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39 References

Citation TypeHas PDFAuthorMore FiltersMore FiltersFiltersSort by RelevanceSort by Most Influenced PapersSort by Citation CountSort by Recency

On the global attractivity and the periodic character of a recursive sequence

    E. ElsayedMathematics
  • 2010
In this paper we investigate the global convergence result, boundedness, and periodicity of solutions of the recursive sequence xn+1 = axn + bx n 1 + cxn 2 dxn 1 + exn 2 , n = 0, 1,..., where the… Expand
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Global asymptotic stability in a rational recursive sequence

    Xiaofan YangH. LaiD. J. EvansG. MegsonMathematicsAppl. Math. Comput.
  • 2004
  • 21
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  • 1 Excerpt
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On The Dynamics Of A Recursive Sequence

    Saniye ErginR. KaratasMathematicsArs Comb.
  • 2013
  • 18
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Dynamics of a higher-order rational difference equation

    M. DehghanR. Mazrooei-SebdaniMathematicsAppl. Math. Comput.
  • 2006
  • 45
  • 1 Excerpt
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Dynamics of a rational difference equation

    E. ElabbasyE. ElsayedMathematics
  • 2009
AbstractThe authors investigate the global behavior of the solutions of the difference equation $$ x_{n + 1} = \frac{{ax_{n - l} x_{n - k} }} {{bx_{n - p} + cx_{n - q} }}, n = 0, 1, \cdots , $$ where… Expand
  • 26
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On the recursive sequencexn+1=α-(xn/xn−1)

    Xingjie YanWan-Tong LiZhu ZhaoMathematics
  • 2005
AbstractWe study the global asymptotic stability, global attractivity, boundedness character, and periodic nature of all positive solutions and all negative solutions of the difference equation… Expand
  • 28
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Dynamics of a rational difference equation

    M. AloqeiliMathematicsAppl. Math. Comput.
  • 2006
  • 77
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The Asymptotic Stability of xn+1 − axn + bxn−k = 0

    Spiridon A. KuruklisMathematics
  • 1994
We obtain necessary and sufficient conditions for the asymptotic stability of the difference equation xn+1 − axn + bxn−k = 0, n = 0, 1, 2, ..., where the coefficients a and b are real numbers and the… Expand
  • 187
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Periodicities in Nonlinear Difference Equations

    E. GroveG. LadasMathematics
  • 2004
PRELIMINARIES EQUATIONS WITH PERIODIC SOLUTIONS EQUATIONS WITH EVENTUALLY PERIODIC SOLUTIONS CONVERGENCE TO PERIODIC SOLUTIONS THE EQUATION x(n+1) = a + gx(n!-(2k+1) )+ d(xn-2l )/ A + x(n-2l) MAX… Expand
  • 429
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  • 1 Excerpt
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On the asymptotic stability of xn+1=(a+xnxn-k)/(xn+xn-k)

    R. Abu-SarisC. ÇinarI. YalçinkayaMathematicsComput. Math. Appl.
  • 2008
  • 33
  • 1 Excerpt
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