Year 2020,
, 155 - 163, 21.12.2020
Burak Oğul
,
Dağistan Şimşek
References
- [1]. Amleh A. M., Grove E. A., Ladas G., Georgiou D. A., On the recursive sequence Anal. Appl., 233, 2, (1999),790-798.
- [2]. Ari, M , elı şken, A., Periodic and asymptotic behavior of a difference equation. Asian-European Journal of Mathematics, 12, 6, (2019), 2040004.
- [3]. Belhannache, F., Nouressadat T., and Raafat A., Dynamics of a third-order rational difference equation, Bull. Math. Soc. Sci. Math. Roumanie, 59, 1, (2016).
- [4]. Cinar C., On the positive solutions of the difference equation x(n+1) = x(n-1) / [1+a x(n) x(n-1)], Appl. Math. Comp., 158, 3, (2004), 809–812.
- [5]. Cinar C., On the positive solutions of the difference equation x(n+1) = x(n-1) / [-1+a x(n) x(n-1)], Appl. Math. Comp., 158, 3, (2004), 793–797.
- [6]. Cinar C., On the positive solutions of the difference equation x(n+1) = a x(n-1) / [1+b x(n) x(n-1)], Appl. Math. Comp., 156, 3, (2004), 587–590.
- [7]. Cı nar, , elı şken, A , Özkan, O , Well-defined solutions of the difference equation xn= xn− 3 kxn− 4 kxn− 5 kxn− kxn− 2 k (±1±xn− 3 kxn− 4 kxn− 5 k) Asian-European Journal of Mathematics, 12, 6, (2019), 2040016.
- [8]. DeVault R., Ladas G., Schultz W.S., On the recursive sequence , Proc. Amer. Math. Soc., 126, 11, (1998), 3257-3261.
- [9]. Elabbasy E. M., El-Metwally H., Elsayed E. M., On the difference equation , Advances in Difference Equation, (2006), 1-10.
- 10]. Elabbasy E. M., El-Metwally H., Elsayed E. M., Qualitative behavior of higher order difference equation, Soochow Journal of Mathematics, 33, 4, (2007), 861-873.
- [11]. Elabbasy E. M., El-Metwally H., Elsayed E. M., Global attractivity and periodic character of a fractional difference equation of order three, Yokohama Mathematical Journal, 53, (2007), 89-100.
- [12]. Elabbasy E. M., El-Metwally H., Elsayed E. M., On the difference equation, J. Conc. Appl. Math., 5(2), (2007), 101-113.
- [13]. Elabbasy E. M. and Elsayed E. M., On the Global Attractivity of Difference Equation of Higher Order, Carpathian Journal of Mathematics, 24, 2, (2008), 45–53.
- [14]. Elsayed E. M., On the Solution of Recursive Sequence of Order Two, Fasciculi Mathematici, 40, (2008), 5–13.
- [15]. Elsayed E. M., Dynamics of a rational recursive sequences. International Journal of Difference Equations, 4, 2, 185–200, 2009.
- [16]. Elsayed E. M., Dynamics of a Recursive Sequence of Higher Order, Communications on Applied Nonlinear Analysis, 16, 2, (2009), 37–50.
- [17]. Elsayed E. M., Solution and atractivity for a rational recursive sequence, Discrete Dynamics in Nature and Society, (2011), 17.
- [18]. Elsayed E. M., On the solution of some difference equation, Europan Journal of Pure and Applied Mathematics, 4, 3, (2011), 287–303.
- [19]. Elsayed E. M., On the Dynamics of a higher order rational recursive sequence, Communications in Mathematical Analysis, 12, 1, (2012), 117–133.
- [20]. Elsayed E. M., Solution of rational difference system of order two, Mathematical and Computer Modelling, 55, (2012), 378–384.
- [21]. Gelisken A., On A System of Rational Difference Equations, J. Comput. Anal. Appl, 23, 4, (2017), 593-606.
- [22]. Gibbons C H , Kulenović M R S and Ladas , On the recursive sequence, Math. Sci. Res. Hot-Line, 4, 2, (2000), 1-11.
- [23]. Ibrahim, T. F., Periodicity and analytic solution of a recursive sequence with numerical examples, Journal of Interdisciplinary Mathematics, 12, 5, (2009), 701-708.
- [24]. Ibrahim, T. F. On the third order rational difference equation, Int. J. Contemp. Math. Sciences 4, 27, (2009), 1321-1334.
- [25]. Ibrahim, T. F., and Touafek, N., On a third order rational difference equation with variable coefficients, DCDIS Series B: Applications & Algorithms 20, (2013), 251-264.
- [26]. Ibrahim T. F., Periodicity and Global Attractivity of Difference Equation of Higher Order, Journal of Computational Analysis & Applications, 16, 1, (2014).
- [27]. Khaliq A., Alzahrani F., and Elsayed E. M., Global attractivity of a rational difference equation of order ten, J. Nonlinear Sci. Appl, 9, 6, (2016), 4465-4477.
On the Recursive Sequence x(n+!) = x(n-14) / [1 + x(n-2) x(n-5) x(n-8) x(n-11)]
Year 2020,
, 155 - 163, 21.12.2020
Burak Oğul
,
Dağistan Şimşek
Abstract
In this paper, given solutions fort he following difference equation
x(n+!) = x(n-14) / [1 + x(n-2) x(n-5) x(n-8) x(n-11)]
where the initial conditions are positive real numbers. The initial conditions of the equation are arbitrary positive real numbers. We investigate periodic behavior of this equation. Also some numerical examples and graphs of solutions are given.
References
- [1]. Amleh A. M., Grove E. A., Ladas G., Georgiou D. A., On the recursive sequence Anal. Appl., 233, 2, (1999),790-798.
- [2]. Ari, M , elı şken, A., Periodic and asymptotic behavior of a difference equation. Asian-European Journal of Mathematics, 12, 6, (2019), 2040004.
- [3]. Belhannache, F., Nouressadat T., and Raafat A., Dynamics of a third-order rational difference equation, Bull. Math. Soc. Sci. Math. Roumanie, 59, 1, (2016).
- [4]. Cinar C., On the positive solutions of the difference equation x(n+1) = x(n-1) / [1+a x(n) x(n-1)], Appl. Math. Comp., 158, 3, (2004), 809–812.
- [5]. Cinar C., On the positive solutions of the difference equation x(n+1) = x(n-1) / [-1+a x(n) x(n-1)], Appl. Math. Comp., 158, 3, (2004), 793–797.
- [6]. Cinar C., On the positive solutions of the difference equation x(n+1) = a x(n-1) / [1+b x(n) x(n-1)], Appl. Math. Comp., 156, 3, (2004), 587–590.
- [7]. Cı nar, , elı şken, A , Özkan, O , Well-defined solutions of the difference equation xn= xn− 3 kxn− 4 kxn− 5 kxn− kxn− 2 k (±1±xn− 3 kxn− 4 kxn− 5 k) Asian-European Journal of Mathematics, 12, 6, (2019), 2040016.
- [8]. DeVault R., Ladas G., Schultz W.S., On the recursive sequence , Proc. Amer. Math. Soc., 126, 11, (1998), 3257-3261.
- [9]. Elabbasy E. M., El-Metwally H., Elsayed E. M., On the difference equation , Advances in Difference Equation, (2006), 1-10.
- 10]. Elabbasy E. M., El-Metwally H., Elsayed E. M., Qualitative behavior of higher order difference equation, Soochow Journal of Mathematics, 33, 4, (2007), 861-873.
- [11]. Elabbasy E. M., El-Metwally H., Elsayed E. M., Global attractivity and periodic character of a fractional difference equation of order three, Yokohama Mathematical Journal, 53, (2007), 89-100.
- [12]. Elabbasy E. M., El-Metwally H., Elsayed E. M., On the difference equation, J. Conc. Appl. Math., 5(2), (2007), 101-113.
- [13]. Elabbasy E. M. and Elsayed E. M., On the Global Attractivity of Difference Equation of Higher Order, Carpathian Journal of Mathematics, 24, 2, (2008), 45–53.
- [14]. Elsayed E. M., On the Solution of Recursive Sequence of Order Two, Fasciculi Mathematici, 40, (2008), 5–13.
- [15]. Elsayed E. M., Dynamics of a rational recursive sequences. International Journal of Difference Equations, 4, 2, 185–200, 2009.
- [16]. Elsayed E. M., Dynamics of a Recursive Sequence of Higher Order, Communications on Applied Nonlinear Analysis, 16, 2, (2009), 37–50.
- [17]. Elsayed E. M., Solution and atractivity for a rational recursive sequence, Discrete Dynamics in Nature and Society, (2011), 17.
- [18]. Elsayed E. M., On the solution of some difference equation, Europan Journal of Pure and Applied Mathematics, 4, 3, (2011), 287–303.
- [19]. Elsayed E. M., On the Dynamics of a higher order rational recursive sequence, Communications in Mathematical Analysis, 12, 1, (2012), 117–133.
- [20]. Elsayed E. M., Solution of rational difference system of order two, Mathematical and Computer Modelling, 55, (2012), 378–384.
- [21]. Gelisken A., On A System of Rational Difference Equations, J. Comput. Anal. Appl, 23, 4, (2017), 593-606.
- [22]. Gibbons C H , Kulenović M R S and Ladas , On the recursive sequence, Math. Sci. Res. Hot-Line, 4, 2, (2000), 1-11.
- [23]. Ibrahim, T. F., Periodicity and analytic solution of a recursive sequence with numerical examples, Journal of Interdisciplinary Mathematics, 12, 5, (2009), 701-708.
- [24]. Ibrahim, T. F. On the third order rational difference equation, Int. J. Contemp. Math. Sciences 4, 27, (2009), 1321-1334.
- [25]. Ibrahim, T. F., and Touafek, N., On a third order rational difference equation with variable coefficients, DCDIS Series B: Applications & Algorithms 20, (2013), 251-264.
- [26]. Ibrahim T. F., Periodicity and Global Attractivity of Difference Equation of Higher Order, Journal of Computational Analysis & Applications, 16, 1, (2014).
- [27]. Khaliq A., Alzahrani F., and Elsayed E. M., Global attractivity of a rational difference equation of order ten, J. Nonlinear Sci. Appl, 9, 6, (2016), 4465-4477.