Yıl: 2021 Cilt: 4 Sayı: 2 Sayfa Aralığı: 89 - 102 Metin Dili: İngilizce DOI: 10.33187/jmsm.929981 İndeks Tarihi: 29-07-2022

Dynamics and Expression of Solution of a Sixth Order Difference Equation

Öz:
This paper deals with the solution behavior and periodic nature of the solutions of the difference equation $$ s_{n+1}=alpha s_{n}+dfrac{beta s_{n}s_{n-4}}{gamma s_{n-4}+delta s_{n-5} },;;;n=0,1,... $$ {Large noindent }where the initial conditions $s_{-5}, s_{-4}, s_{-3}, s_{-2}, s_{-1}, s_{0}$ are arbitrary positive real numbers and $alpha , beta , gamma , delta $are positive constants. Also we obtain the closed form of the solutions of some special cases of this equation.
Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • [1] R.E. Mickens, Difference Equations, Van Nostrand Reinhold Comp, New York, 1987.
  • [2] M.C. Mackey, L. Glass, Oscillation and chaos in physiological control system, Science, 197(1977), 287-289.
  • [3] M.R.S. Kulenovic, G. Ladas, Dynamics of Second Order Rational Difference Equations with Open Problems and Conjectures, Chapman & Hall / CRC Press, 2001.
  • [4] R.J. Beverton, S.J. Holt, On the Dynamics of Exploited Fish Populations, Fish Invest., London, 1957.
  • [5] R. DeVault, G. Dial, V.L., Kocic, G. Ladas, Global behavior of solutions of xn+1 = axn + f(xn, xn−1), Journal of Difference Equations and Applications, 3(3-4)(1997), 311-330.
  • [6] E.M. Elsayed, Qualitative behaviour of difference equation of order two, Mathematical and Computer Modelling, 50(2009),1130-1141.
  • [7] Elabbasy, E. M. Elsayed, On the difference equation, xn+1 = .αxn−l+βxn−k Axn−l+Bxn−k ,, Acta Mathematica Vietnamica, 33(2008), 85-94.
  • [8] R. Karatas, C. Cinar, D. Simsek, On positive solutions of the difference equation xn+1 = xn−5 1+xn−2xn−5 , Int. J. Contemp. Math. Sci., 1(10)(2006), 495-500.
  • [9] H. El-Metwally, E. M. Elsayed, Dynamics of a rational difference equation xn+1 = axn−lxn−k bxn−p +cxn−q , Chinese Annals of Mathematics series B, 15(5)(2013), 852-857.
  • [10] E. M. Elsayed, Behavior and expression of the solutions of some rational difference equations, Journal of Computational Analysis and Applications, 15(1)(2013), 73-81.
  • [11] M. Saleh, M. Aloqeili, On the difference equation yn+1 = A+ yn yn−k ,, Appl. Math. Comput. 176(1)(2006), 359-363.
  • [12] E. M. Elsayed, A. Khaliq, Global attractivity and periodicity behavior of a recursive sequence, J. Comput. Anal. Appl., 22(2)(2017), 369-379. [13] C. Cinar, On the positive solutions of the difference equation xn+1 = axn−1 1+bxnxn−1 , Appl. Math. Comp., 156(2004) 587-590.
  • [14] S. E. Das, M.Bayram, On a System of Rational Difference Equations, World Applied Sciences Journal, 10(11)(2010), 1306-1312.
  • [15] Q. Din, E. M. Elsayed, Stability analysis of a discrete ecological model, Computational Ecology and Software, 4(2)(2014), 89-103.
  • [16] E. M. Elabbasy, H. El-Metwally, E. M. Elsayed, On the difference equations xn+1 = αxn−k β +γ ∏ k i=0 xn−i , J. Conc. Appl. Math., 5(2) (2007), 101-113.
  • [17] E. M. Elabbasy, H. El-Metwally, E. M. Elsayed, Qualitative behavior of higher order difference equation, Soochow Journal of Mathematics, 33(4)(2007),
  • [18] E. M. Elabbasy, H. El-Metwally, E. M. Elsayed, On the Difference Equation xn+1 = 861-873. a0xn+a1xn−1+...+ak xn−k b0xn+b1xn−1+...+bk xn−k , Mathematica Bohemica, 133(2) (2008), 133-147.
  • [19] R. Agarwal, Difference equations and inequalities, Theory, methods and applications, Marcel Dekker Inc., New York, 1992.
  • [20] H. Chen, H. Wang, Global attractivity of the difference equation xn+1 = xn +αxn−1 β +xn , Appl. Math. Comp., 181(2006),1431-1438.
  • [21] E. M. Elsayed, Dynamics of a Recursive Sequence of Higher Order, Communications on Applied Nonlinear Analysis, 16(2)(2009), 37-50.
  • [22] A. Khaliq, E. M. Elsayed, The Dynamics and Solution of some Difference Equations, Journal of Nonlinear Sciences and Applications, 9(3) (2016), 1052-1063.
  • [23] A. Khaliq, On the Solution and Periodic Nature of Higher-order Difference Equation, Mathematical Sciences Letters, 6(2)(2017), 177-186.
  • [24] A. Khaliq, E. M. Elsayed, Qualitative properties of difference equation of order six, Mathematics, 4(2016), 24.
  • [25] V. L. Kocic, G. Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Kluwer Academic Publishers, Dordrecht, 1993.
  • [26] A. S. Kurbanli, On the Behavior of Solutions of the System of Rational Difference Equations, World Applied Sciences Journal, 10(11) (2010), 1344-1350.
  • [27] R. Memarbashi, Sufficient conditions for the exponential stability of nonautonomous difference equations, Appl. Math. Letter, 21 (2008), 232-235.
  • [28] A. Neyrameh, H. Neyrameh, M. Ebrahimi, A. Roozi, Analytic solution diffusivity equation in rational form, World Applied Sciences Journal, 10(7)(2010), 764-768.
APA Khaliq A (2021). Dynamics and Expression of Solution of a Sixth Order Difference Equation. , 89 - 102. 10.33187/jmsm.929981
Chicago Khaliq Abdul Dynamics and Expression of Solution of a Sixth Order Difference Equation. (2021): 89 - 102. 10.33187/jmsm.929981
MLA Khaliq Abdul Dynamics and Expression of Solution of a Sixth Order Difference Equation. , 2021, ss.89 - 102. 10.33187/jmsm.929981
AMA Khaliq A Dynamics and Expression of Solution of a Sixth Order Difference Equation. . 2021; 89 - 102. 10.33187/jmsm.929981
Vancouver Khaliq A Dynamics and Expression of Solution of a Sixth Order Difference Equation. . 2021; 89 - 102. 10.33187/jmsm.929981
IEEE Khaliq A "Dynamics and Expression of Solution of a Sixth Order Difference Equation." , ss.89 - 102, 2021. 10.33187/jmsm.929981
ISNAD Khaliq, Abdul. "Dynamics and Expression of Solution of a Sixth Order Difference Equation". (2021), 89-102. https://doi.org/10.33187/jmsm.929981
APA Khaliq A (2021). Dynamics and Expression of Solution of a Sixth Order Difference Equation. Journal of mathematical sciences and modelling (Online), 4(2), 89 - 102. 10.33187/jmsm.929981
Chicago Khaliq Abdul Dynamics and Expression of Solution of a Sixth Order Difference Equation. Journal of mathematical sciences and modelling (Online) 4, no.2 (2021): 89 - 102. 10.33187/jmsm.929981
MLA Khaliq Abdul Dynamics and Expression of Solution of a Sixth Order Difference Equation. Journal of mathematical sciences and modelling (Online), vol.4, no.2, 2021, ss.89 - 102. 10.33187/jmsm.929981
AMA Khaliq A Dynamics and Expression of Solution of a Sixth Order Difference Equation. Journal of mathematical sciences and modelling (Online). 2021; 4(2): 89 - 102. 10.33187/jmsm.929981
Vancouver Khaliq A Dynamics and Expression of Solution of a Sixth Order Difference Equation. Journal of mathematical sciences and modelling (Online). 2021; 4(2): 89 - 102. 10.33187/jmsm.929981
IEEE Khaliq A "Dynamics and Expression of Solution of a Sixth Order Difference Equation." Journal of mathematical sciences and modelling (Online), 4, ss.89 - 102, 2021. 10.33187/jmsm.929981
ISNAD Khaliq, Abdul. "Dynamics and Expression of Solution of a Sixth Order Difference Equation". Journal of mathematical sciences and modelling (Online) 4/2 (2021), 89-102. https://doi.org/10.33187/jmsm.929981