[1] A. E. Hamza, A. M. Ahmed and A. M. Youssef, On the recursive sequence , Arab Journal of Mathematical Sciences.,
17(2011), 31-44.
[2] A. Khaliq and E. M. Elsayed, Qualitative study of a higher order rational difference equation, Hacettepe Journal of Mathematics and Statistics,
47(5)(2018), 1128-1143.
[3] A. Q. Khan, Q. Din, M. N. Qureshi and T F. Ibrahim, Global behavior of an anti-competive system of fourth-order rational difference equations,
Computational Ecology and Software, 4(1)(2014), 35-46.
[4] D. T. Tollu, Y. Yazlik and N. Taskara, On a solvable nonlinear difference equation of higher order, Turkish Journal of Mathematics, 42(4)(2018),
1765-1778.
[5] D. T. Tollu and I. Yalcinkaya, Global behavior of a three-dimensional system of difference equations of order three, Communications Faculty of Sciences
University of Ankara Series A1 Mathematics and Statistics, 681(2019), 1-16.
[6] E. A. Grove and G. Ladas, Periodicities in Nonlinear Difference Equations, Advances in Discrete Mathematics and Applications, Volume 4, Chapman
and Hall, CRS Press, 2005.
[7] E. M. Elabbasy and S. M Elaissawy, Global behavior of a higher-order rational difference equation, Fasciculi Mathematici, 53(2014), 39-52.
[8] E. M. Elsayed, On the dynamics of a higher-order rational recursive sequence, Communications in Mathematical Analysis, 12(2012), 117-133.
[9] E. M. Elsayed and T. F. Ibrahim, Solutions and periodicity of a rational recursive sequences of order five, Bulletin of the Malaysian Mathematical
Sciences Society, 38(2015), 95-112.
[10] F. Belhannache, N. Touafek and R. Abo-Zeid, Dynamics of a third-order rational difference equation, Bulletin Mathematique de la Societe des Sciences
Math´ematiques de Roumanie, 59(1)(2016), 13-22.
[11] F. Belhannache, N. Touafek and R. Abo-Zeid, On a higher order rational difference equation, Journal of Applied Mathematics and Informatics,
5-6(34)(2016), 369-382.
[12] I. Okumus and Y. Soykan, On the solutions of four rational difference equations associated to tribonacci numbers, Konuralp Journal of Mathematics,
8(1)(2020), 79-90.
[13] M. E. Erdogan and C. Cinar, On the dynamics of the recursive sequence x_{n+1}=\alpha x_{n-1}/(\beta +\gamma \Sigma
_{k=1}^{t}x_{n-2k}^{p}\prod_{k=1}^{t}x_{n-2k}^{q}), Fasciculi Mathematici, 50(2013), 59-66.
[14] M. Gümüş¸ and Ö . Öcalan, Global asymptotic stability of a nonautonomous difference equation, Journal of Applied Mathematics, Article ID 395954,
(2014), 5 pages.
[15] M. Gümüş, R. Abo-Zeid and Ö . Öcalan, Dynamical behavior of a third-order difference equation with arbitrary powers, Kyungpook Mathematical
Journal, 57(2017), 251-263.
[16] M. Gümüş¸ and Y. Soykan, The dynamics of positive solutions of a higher order fractional difference equation with arbitrary powers, Journal of Applied
Mathematics and Informatics, 35(2017), 267-276.
[17] M. Gümüş and R. Abo-Zeid, On the solutions of a (2k+2)th order difference equation, Dynamics of Continuous Discrete and Impulsive Systems Series
B: Applications & Algorithms, 25(2018), 129-143.
[18] M. Shojaei, R. Saadati and H. Adbi, Stability and periodic character of a rational third order difference equation, Chaos Solitons and Fractals 39(2009),
1203-1209.
[19] M. R. S. Kulenovic and G. Ladas, Dynamics of Second Order Rational Difference Equations with Open Problems and Conjectures, Chapman and Hall,
CRC Press, 2001.
[20] Q. Din, T. F. Ibrahim and K. A. Khan, Behavior of a competitive system of second-order difference equations, The Scientific World Journal, ID 283982,
(2014), 9 pages.
[21] R. Abo-Zeid, Global behavior of a higher order difference equation, Mathematica Slovaca, 64(4)(2014), 931-940.
[22] S. Elaydi, An Introduction to Difference Equations, Springer, New York, 1999.
[23] T. F. Ibrahim, Periodicity and global attractivity of difference equation of higher order, Journal of Computational Analysis and Applications, 16(3)(2014),
552-564.
[24] V. L. Kocic and G. Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Kluwer Academic Publishers,
Dordrecht, 1993.
[25] Y. Yazlik, D. T. Tollu and N. Taskara, On the behaviour of solutions for some systems of difference equations, Journal of Computational Analysis and
Applications, 18(1)(2015), 166-178.
[26] Y. Yazlik, D. T. Tollu and N. Taskara, Behaviour of solutions for a system of two higher-order difference equations, Journal of Science and Arts,
4(45)(2018), 813-826.
On Dynamics of A Higher-Order Rational Difference Equation
Year 2020,
Volume: 8 Issue: 2, 223 - 228, 27.10.2020
In this paper, we study the dynamical behavior of the positive solutions of the difference equation y_{n+1}=\frac{A+By_{n}}{C+D\prod_{i=1}^{k}y_{n-i}^{q_{i}}},\ n\in \mathbb{N}_{0} where \mathbb{N}_{0}=\mathbb{N} \cup \left\{ 0\right\} , the initial conditions and the parameters A,B are non-negative real numbers, the parameters C, D\ are positive real numbers, q_{i} for i\in \{1,2,...k\} are fixed positive integers and % 1\leq k.
[1] A. E. Hamza, A. M. Ahmed and A. M. Youssef, On the recursive sequence x_{n+1}=(a+bx_{n})/(A+Bx_{n-1}^{k}), Arab Journal of Mathematical Sciences.,
17(2011), 31-44.
[2] A. Khaliq and E. M. Elsayed, Qualitative study of a higher order rational difference equation, Hacettepe Journal of Mathematics and Statistics,
47(5)(2018), 1128-1143.
[3] A. Q. Khan, Q. Din, M. N. Qureshi and T F. Ibrahim, Global behavior of an anti-competive system of fourth-order rational difference equations,
Computational Ecology and Software, 4(1)(2014), 35-46.
[4] D. T. Tollu, Y. Yazlik and N. Taskara, On a solvable nonlinear difference equation of higher order, Turkish Journal of Mathematics, 42(4)(2018),
1765-1778.
[5] D. T. Tollu and I. Yalcinkaya, Global behavior of a three-dimensional system of difference equations of order three, Communications Faculty of Sciences
University of Ankara Series A1 Mathematics and Statistics, 681(2019), 1-16.
[6] E. A. Grove and G. Ladas, Periodicities in Nonlinear Difference Equations, Advances in Discrete Mathematics and Applications, Volume 4, Chapman
and Hall, CRS Press, 2005.
[7] E. M. Elabbasy and S. M Elaissawy, Global behavior of a higher-order rational difference equation, Fasciculi Mathematici, 53(2014), 39-52.
[8] E. M. Elsayed, On the dynamics of a higher-order rational recursive sequence, Communications in Mathematical Analysis, 12(2012), 117-133.
[9] E. M. Elsayed and T. F. Ibrahim, Solutions and periodicity of a rational recursive sequences of order five, Bulletin of the Malaysian Mathematical
Sciences Society, 38(2015), 95-112.
[10] F. Belhannache, N. Touafek and R. Abo-Zeid, Dynamics of a third-order rational difference equation, Bulletin Mathematique de la Societe des Sciences
Math´ematiques de Roumanie, 59(1)(2016), 13-22.
[11] F. Belhannache, N. Touafek and R. Abo-Zeid, On a higher order rational difference equation, Journal of Applied Mathematics and Informatics,
5-6(34)(2016), 369-382.
[12] I. Okumus and Y. Soykan, On the solutions of four rational difference equations associated to tribonacci numbers, Konuralp Journal of Mathematics,
8(1)(2020), 79-90.
[13] M. E. Erdogan and C. Cinar, On the dynamics of the recursive sequence x_{n+1}=\alpha x_{n-1}/(\beta +\gamma \Sigma
_{k=1}^{t}x_{n-2k}^{p}\prod_{k=1}^{t}x_{n-2k}^{q}), Fasciculi Mathematici, 50(2013), 59-66.
[14] M. Gümüş¸ and Ö . Öcalan, Global asymptotic stability of a nonautonomous difference equation, Journal of Applied Mathematics, Article ID 395954,
(2014), 5 pages.
[15] M. Gümüş, R. Abo-Zeid and Ö . Öcalan, Dynamical behavior of a third-order difference equation with arbitrary powers, Kyungpook Mathematical
Journal, 57(2017), 251-263.
[16] M. Gümüş¸ and Y. Soykan, The dynamics of positive solutions of a higher order fractional difference equation with arbitrary powers, Journal of Applied
Mathematics and Informatics, 35(2017), 267-276.
[17] M. Gümüş and R. Abo-Zeid, On the solutions of a (2k+2)th order difference equation, Dynamics of Continuous Discrete and Impulsive Systems Series
B: Applications & Algorithms, 25(2018), 129-143.
[18] M. Shojaei, R. Saadati and H. Adbi, Stability and periodic character of a rational third order difference equation, Chaos Solitons and Fractals 39(2009),
1203-1209.
[19] M. R. S. Kulenovic and G. Ladas, Dynamics of Second Order Rational Difference Equations with Open Problems and Conjectures, Chapman and Hall,
CRC Press, 2001.
[20] Q. Din, T. F. Ibrahim and K. A. Khan, Behavior of a competitive system of second-order difference equations, The Scientific World Journal, ID 283982,
(2014), 9 pages.
[21] R. Abo-Zeid, Global behavior of a higher order difference equation, Mathematica Slovaca, 64(4)(2014), 931-940.
[22] S. Elaydi, An Introduction to Difference Equations, Springer, New York, 1999.
[23] T. F. Ibrahim, Periodicity and global attractivity of difference equation of higher order, Journal of Computational Analysis and Applications, 16(3)(2014),
552-564.
[24] V. L. Kocic and G. Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Kluwer Academic Publishers,
Dordrecht, 1993.
[25] Y. Yazlik, D. T. Tollu and N. Taskara, On the behaviour of solutions for some systems of difference equations, Journal of Computational Analysis and
Applications, 18(1)(2015), 166-178.
[26] Y. Yazlik, D. T. Tollu and N. Taskara, Behaviour of solutions for a system of two higher-order difference equations, Journal of Science and Arts,
4(45)(2018), 813-826.
Güler, M., Yalçınkaya, İ., & Belhannache, F. (2020). On Dynamics of A Higher-Order Rational Difference Equation. Konuralp Journal of Mathematics, 8(2), 223-228.
AMA
Güler M, Yalçınkaya İ, Belhannache F. On Dynamics of A Higher-Order Rational Difference Equation. Konuralp J. Math. October 2020;8(2):223-228.
Chicago
Güler, Memiş, İbrahim Yalçınkaya, and Farida Belhannache. “On Dynamics of A Higher-Order Rational Difference Equation”. Konuralp Journal of Mathematics 8, no. 2 (October 2020): 223-28.
EndNote
Güler M, Yalçınkaya İ, Belhannache F (October 1, 2020) On Dynamics of A Higher-Order Rational Difference Equation. Konuralp Journal of Mathematics 8 2 223–228.
IEEE
M. Güler, İ. Yalçınkaya, and F. Belhannache, “On Dynamics of A Higher-Order Rational Difference Equation”, Konuralp J. Math., vol. 8, no. 2, pp. 223–228, 2020.
ISNAD
Güler, Memiş et al. “On Dynamics of A Higher-Order Rational Difference Equation”. Konuralp Journal of Mathematics 8/2 (October 2020), 223-228.
JAMA
Güler M, Yalçınkaya İ, Belhannache F. On Dynamics of A Higher-Order Rational Difference Equation. Konuralp J. Math. 2020;8:223–228.
MLA
Güler, Memiş et al. “On Dynamics of A Higher-Order Rational Difference Equation”. Konuralp Journal of Mathematics, vol. 8, no. 2, 2020, pp. 223-8.
Vancouver
Güler M, Yalçınkaya İ, Belhannache F. On Dynamics of A Higher-Order Rational Difference Equation. Konuralp J. Math. 2020;8(2):223-8.