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Year 2019, Volume: 7 Issue: 2, 147 - 156, 25.12.2019

Dağıstan Şimşek , Burak Oğul

Abstract

References

  • [1] Amleh A. M., Grove E. A., Ladas G., Georgiou D. A., On the recursive sequence , J. Math. Anal. Appl., 233, no. 2, (1999),790-798.
  • [2] Belhannache, F., Nouressadat T., and Raafat A., Dynamics of a third-order rational difference equation, Bull. Math. Soc. Sci. Math. Roumanie, 59 (1), (2016).
  • [3] Cinar C., On the positive solutions of the difference equation , Appl. Math. Comp., 158 (3), (2004), 809–812.
  • [4] Cinar C., On the positive solutions of the difference equation , Appl. Math. Comp., 158 (3), (2004), 793–797.
  • [5] Cinar C., On the positive solutions of the difference equation , Appl. Math. Comp., 156 (3), (2004), 587–590.
  • [6] DeVault R., Ladas G. and Schultz W.S., On the recursive sequence , Proc. Amer. Math. Soc., 126 no. 11, (1998), 3257-3261.
  • [7] Elabbasy E. M., El-Metwally H., Elsayed E. M., On the difference equation , Advances in Difference Equation, (2006), 1-10.
  • [8] 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.
  • [9] 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.
  • [10] Elabbasy E. M., El-Metwally H., Elsayed E. M., On the difference equation , J. Conc. Appl. Math., 5(2), (2007), 101-113.
  • [11] 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.
  • [12] Elsayed E. M., On the Solution of Recursive Sequence of Order Two, Fasciculi Mathematici, 40, (2008), 5–13.
  • [13] Elsayed E. M., Dynamics of a rational recursive sequences. International Journal of Difference Equations, 4(2), 185–200, 2009.
  • [14] Elsayed E. M., Dynamics of a Recursive Sequence of Higher Order, Communications on Applied Nonlinear Analysis, 16 (2), (2009), 37–50.
  • [15] Elsayed E. M., Solution and atractivity for a rational recursive sequence, Discrete Dynamics in Nature and Society, (2011), 17.
  • [16] Elsayed E. M., On the solution of some difference equation, Europan Journal of Pure and Applied Mathematics, 4 (3), (2011), 287–303.
  • [17] Elsayed E. M., On the Dynamics of a higher order rational recursive sequence, Communications in Mathematical Analysis, 12 (1), (2012), 117–133.
  • [18] Elsayed E. M., Solution of rational difference system of order two, Mathematical and Computer Modelling, 55, (2012), 378–384.
  • [19] Gibbons C. H., Kulenović M. R. S. and Ladas G., On the recursive sequence , Math. Sci. Res. Hot-Line, 4 (2), (2000), 1-11.
  • [20] Ibrahim, T. F., Periodicity and analytic solution of a recursive sequence with numerical examples, Journal of Interdisciplinary Mathematics, 12 (5), (2009), 701-708.
  • [21] Ibrahim, T. F. On the third order rational difference equation, Int. J. Contemp. Math. Sciences 4 (27), (2009), 1321-1334.
  • [22] 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.
  • [23] Ibrahim, T. F., Periodicity and Global Attractivity of Difference Equation of Higher Order, Journal of Computational Analysis & Applications, 16 (1), (2014).
  • [24] 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.
  • [25] Kulenović M.R.S., Ladas G., Sizer W.S., On the recursive sequence Math. Sci. Res. Hot-Line, 2, 5, (1998), 1-16.
  • [26] Kulenovic, M. R. S., Moranjkic, S., and Nurkanovic, Z., Naimark-Sacker bifurcation of second order rational difference equation with quadratic terms., J. Nonlinear Sci. Appl, 10, (2017), 3477-3489.
  • [27] Stevic S., On the recursive sequence , Taiwanese J. Math., 6, 3, (2002), 405-414.
  • [28] Simsek D., Cinar C. and Yalcinkaya I., On the recursive sequence , Int. J. Contemp. Math. Sci., 1, 9-12, (2006), 475-480.
  • [29] Simsek D., Cinar C., Karatas R., Yalcinkaya I., On the recursive sequence , Int. J. Pure Appl. Math., 27, 4, (2006), 501-507.
  • [30] Simsek D., Cinar C., Karatas R., Yalcinkaya I., "n the recursive sequence , Int. J. Pure Appl. Math., 28, 1, (2006), 117-124.
  • [31] Simsek D., Cinar C., Yalcinkaya I., On The Recursive Sequence x(n+1) = x[n-(5k+9)] / 1+x(n-4)x(n-9) x[n-(5k+4)], Taiwanese Journal of Mathematics, Vol. 12, 5, (2008), 1087-1098.
  • [32] Simsek D., Dogan A., On A Class of Recursive Sequence, Manas Journal of Engineering, 2, 1, (2014), 16-22.
  • [33] Simsek D., Eröz M., Solutions of The Rational Difference Equations , Manas Journal of Engineering, 4, 1, (2016), 12-20.
  • [34] Simsek D., Oğul B., Solutions of The Rational Difference Equations , Manas Journal of Engineering, 5, 3, (2017), 57-68.
  • [35] Şimşek D., Oğul B., Abdullayev F., Solutions of The Rational Difference Equations , AIP Conference Proceedings, 1880(1), 040003, (2017).
  • [36] Simsek D., Abdullayev F., On The Recursive Sequence , Journal of Mathematics Sciences, Vol. 6, No. 222, (2017), 762-771.
  • [37] Simsek, D., Abdullayev, F. G., On the Recursive Sequence , Journal of Mathematical Sciences, 234 (1), (2018), 73-81.
  • [38] Takahasi, S., Yasuhide, M., and Takeshi, M., On Convergence of a Recursıve Sequence x_ {n+ 1}= f (x_ {n-1}, x_n), Taiwanese Journal of Mathematics, 10 (3), (2006), 631-638.
  • [39] Yan, X., Wan-Tong, L., and Zhu Z., On the recursive sequencex n+ 1= α-(x n/x n− 1), Journal of Applied Mathematics and Computing, 17 (1), (2005), 269-282.
  • [40] Zhang, L., Guang Z., and Hui, L., Periodicity and attractivity for a rational recursive sequence, Journal of Applied Mathematics and Computing 19 (1-2), (2005), 191-201.

On The Recursive Sequence x(n+1)=x(n-20)/[1+x(n-2)x(n-5)x(n-8)x(n-11)x(n-14)x(n-17)]

Year 2019, Volume: 7 Issue: 2, 147 - 156, 25.12.2019

Dağıstan Şimşek , Burak Oğul

Abstract



The behaivour of the solutions of the following system of
difference equations is examined,



x(n+1)=x(n-20)/[1+x(n-2)x(n-5)x(n-8)x(n-11)x(n-14)x(n-17)] 



where the initial conditions are positive real numbers.
The initial conditions of the equation are arbitrary positive real numbers.
Also, we discuss and illustrate the stability of the solutions in the
neighborhood of the critical points and the periodicity of the considered
equations. 



Keywords

Difference equation rational difference equation period 21 solutions

References

  • [1] Amleh A. M., Grove E. A., Ladas G., Georgiou D. A., On the recursive sequence , J. Math. Anal. Appl., 233, no. 2, (1999),790-798.
  • [2] Belhannache, F., Nouressadat T., and Raafat A., Dynamics of a third-order rational difference equation, Bull. Math. Soc. Sci. Math. Roumanie, 59 (1), (2016).
  • [3] Cinar C., On the positive solutions of the difference equation , Appl. Math. Comp., 158 (3), (2004), 809–812.
  • [4] Cinar C., On the positive solutions of the difference equation , Appl. Math. Comp., 158 (3), (2004), 793–797.
  • [5] Cinar C., On the positive solutions of the difference equation , Appl. Math. Comp., 156 (3), (2004), 587–590.
  • [6] DeVault R., Ladas G. and Schultz W.S., On the recursive sequence , Proc. Amer. Math. Soc., 126 no. 11, (1998), 3257-3261.
  • [7] Elabbasy E. M., El-Metwally H., Elsayed E. M., On the difference equation , Advances in Difference Equation, (2006), 1-10.
  • [8] 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.
  • [9] 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.
  • [10] Elabbasy E. M., El-Metwally H., Elsayed E. M., On the difference equation , J. Conc. Appl. Math., 5(2), (2007), 101-113.
  • [11] 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.
  • [12] Elsayed E. M., On the Solution of Recursive Sequence of Order Two, Fasciculi Mathematici, 40, (2008), 5–13.
  • [13] Elsayed E. M., Dynamics of a rational recursive sequences. International Journal of Difference Equations, 4(2), 185–200, 2009.
  • [14] Elsayed E. M., Dynamics of a Recursive Sequence of Higher Order, Communications on Applied Nonlinear Analysis, 16 (2), (2009), 37–50.
  • [15] Elsayed E. M., Solution and atractivity for a rational recursive sequence, Discrete Dynamics in Nature and Society, (2011), 17.
  • [16] Elsayed E. M., On the solution of some difference equation, Europan Journal of Pure and Applied Mathematics, 4 (3), (2011), 287–303.
  • [17] Elsayed E. M., On the Dynamics of a higher order rational recursive sequence, Communications in Mathematical Analysis, 12 (1), (2012), 117–133.
  • [18] Elsayed E. M., Solution of rational difference system of order two, Mathematical and Computer Modelling, 55, (2012), 378–384.
  • [19] Gibbons C. H., Kulenović M. R. S. and Ladas G., On the recursive sequence , Math. Sci. Res. Hot-Line, 4 (2), (2000), 1-11.
  • [20] Ibrahim, T. F., Periodicity and analytic solution of a recursive sequence with numerical examples, Journal of Interdisciplinary Mathematics, 12 (5), (2009), 701-708.
  • [21] Ibrahim, T. F. On the third order rational difference equation, Int. J. Contemp. Math. Sciences 4 (27), (2009), 1321-1334.
  • [22] 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.
  • [23] Ibrahim, T. F., Periodicity and Global Attractivity of Difference Equation of Higher Order, Journal of Computational Analysis & Applications, 16 (1), (2014).
  • [24] 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.
  • [25] Kulenović M.R.S., Ladas G., Sizer W.S., On the recursive sequence Math. Sci. Res. Hot-Line, 2, 5, (1998), 1-16.
  • [26] Kulenovic, M. R. S., Moranjkic, S., and Nurkanovic, Z., Naimark-Sacker bifurcation of second order rational difference equation with quadratic terms., J. Nonlinear Sci. Appl, 10, (2017), 3477-3489.
  • [27] Stevic S., On the recursive sequence , Taiwanese J. Math., 6, 3, (2002), 405-414.
  • [28] Simsek D., Cinar C. and Yalcinkaya I., On the recursive sequence , Int. J. Contemp. Math. Sci., 1, 9-12, (2006), 475-480.
  • [29] Simsek D., Cinar C., Karatas R., Yalcinkaya I., On the recursive sequence , Int. J. Pure Appl. Math., 27, 4, (2006), 501-507.
  • [30] Simsek D., Cinar C., Karatas R., Yalcinkaya I., "n the recursive sequence , Int. J. Pure Appl. Math., 28, 1, (2006), 117-124.
  • [31] Simsek D., Cinar C., Yalcinkaya I., On The Recursive Sequence x(n+1) = x[n-(5k+9)] / 1+x(n-4)x(n-9) x[n-(5k+4)], Taiwanese Journal of Mathematics, Vol. 12, 5, (2008), 1087-1098.
  • [32] Simsek D., Dogan A., On A Class of Recursive Sequence, Manas Journal of Engineering, 2, 1, (2014), 16-22.
  • [33] Simsek D., Eröz M., Solutions of The Rational Difference Equations , Manas Journal of Engineering, 4, 1, (2016), 12-20.
  • [34] Simsek D., Oğul B., Solutions of The Rational Difference Equations , Manas Journal of Engineering, 5, 3, (2017), 57-68.
  • [35] Şimşek D., Oğul B., Abdullayev F., Solutions of The Rational Difference Equations , AIP Conference Proceedings, 1880(1), 040003, (2017).
  • [36] Simsek D., Abdullayev F., On The Recursive Sequence , Journal of Mathematics Sciences, Vol. 6, No. 222, (2017), 762-771.
  • [37] Simsek, D., Abdullayev, F. G., On the Recursive Sequence , Journal of Mathematical Sciences, 234 (1), (2018), 73-81.
  • [38] Takahasi, S., Yasuhide, M., and Takeshi, M., On Convergence of a Recursıve Sequence x_ {n+ 1}= f (x_ {n-1}, x_n), Taiwanese Journal of Mathematics, 10 (3), (2006), 631-638.
  • [39] Yan, X., Wan-Tong, L., and Zhu Z., On the recursive sequencex n+ 1= α-(x n/x n− 1), Journal of Applied Mathematics and Computing, 17 (1), (2005), 269-282.
  • [40] Zhang, L., Guang Z., and Hui, L., Periodicity and attractivity for a rational recursive sequence, Journal of Applied Mathematics and Computing 19 (1-2), (2005), 191-201.
There are 40 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Article
Authors

Dağıstan Şimşek

Burak Oğul 0000-0002-3264-4340

Publication Date December 25, 2019
Published in Issue Year 2019 Volume: 7 Issue: 2

Cite

APA Şimşek, D., & Oğul, B. (2019). On The Recursive Sequence x(n+1)=x(n-20)/[1+x(n-2)x(n-5)x(n-8)x(n-11)x(n-14)x(n-17)]. MANAS Journal of Engineering, 7(2), 147-156.
AMA Şimşek D, Oğul B. On The Recursive Sequence x(n+1)=x(n-20)/[1+x(n-2)x(n-5)x(n-8)x(n-11)x(n-14)x(n-17)]. MJEN. December 2019;7(2):147-156.
Chicago Şimşek, Dağıstan, and Burak Oğul. “On The Recursive Sequence x(n+1)=x(n-20)/[1+x(n-2)x(n-5)x(n-8)x(n-11)x(n-14)x(n-17)]”. MANAS Journal of Engineering 7, no. 2 (December 2019): 147-56.
EndNote Şimşek D, Oğul B (December 1, 2019) On The Recursive Sequence x(n+1)=x(n-20)/[1+x(n-2)x(n-5)x(n-8)x(n-11)x(n-14)x(n-17)]. MANAS Journal of Engineering 7 2 147–156.
IEEE D. Şimşek and B. Oğul, “On The Recursive Sequence x(n+1)=x(n-20)/[1+x(n-2)x(n-5)x(n-8)x(n-11)x(n-14)x(n-17)]”, MJEN, vol. 7, no. 2, pp. 147–156, 2019.
ISNAD Şimşek, Dağıstan - Oğul, Burak. “On The Recursive Sequence x(n+1)=x(n-20)/[1+x(n-2)x(n-5)x(n-8)x(n-11)x(n-14)x(n-17)]”. MANAS Journal of Engineering 7/2 (December 2019), 147-156.
JAMA Şimşek D, Oğul B. On The Recursive Sequence x(n+1)=x(n-20)/[1+x(n-2)x(n-5)x(n-8)x(n-11)x(n-14)x(n-17)]. MJEN. 2019;7:147–156.
MLA Şimşek, Dağıstan and Burak Oğul. “On The Recursive Sequence x(n+1)=x(n-20)/[1+x(n-2)x(n-5)x(n-8)x(n-11)x(n-14)x(n-17)]”. MANAS Journal of Engineering, vol. 7, no. 2, 2019, pp. 147-56.
Vancouver Şimşek D, Oğul B. On The Recursive Sequence x(n+1)=x(n-20)/[1+x(n-2)x(n-5)x(n-8)x(n-11)x(n-14)x(n-17)]. MJEN. 2019;7(2):147-56.
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