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ON THE PERIODICITY OF SOLUTIONS OF A SYSTEM OF RATIONAL DIFFERENCE EQUATIONS

Year 2020, Volume: 2 Issue: 2, 1 - 8, 30.10.2020

Abstract

In this paper, we have investigated the periodicity of the well-defined solutions of the system of difference equations u(n+1)=(u(n-1)+v(n))/(alpha*(u(n-1)*v(n)-1) , v(n+1)=(v(n-1)+u(n))/(alpha*(v(n-1)*u(n)-1), w(n+1)=u(n)/v(n)
where u(0), u(-1), v(0), v(-1), w(0), w(-1) non zore reel numbers and alpha positive reel numbers. In this paper, we have investigated the periodicity of the well-defined solutions of the system of difference equations u(n+1)=(u(n-1)+v(n))/(alpha*(u(n-1)*v(n)-1) , v(n+1)=(v(n-1)+u(n))/(alpha*(v(n-1)*u(n)-1), w(n+1)=u(n)/v(n)
where u(0), u(-1), v(0), v(-1), w(0), w(-1) non zore reel numbers and alpha positive reel numbers.

References

  • [1] Akgüneş, N., Kurbanli, A. S. (2014) On the system of rational difference equations x(n)=f((x(n-a(1)), y(n-a(1))), y(n)=g((y(n-a(1)), z(n-a(1))), z(n)=h((z(n-a(1)), x(n-a(1))), Selcuk Journal of Applied Mathematics, 15(1): 8 pages.
  • [2] Camouzis, E., Papaschinopoulos, G. (2004) Global asymptotic behavior of positive solutions of the system of rational difference equations x(n+1)=(1+(x(n)/y(n-m)), y(n+1)=(1+(y(n)/x(n-m)), Applied Mathematics Letters, 17:733-737.
  • [3] Çinar, C. (2004) On the positive solutions of the difference equation system x(n+1)=(1/y(n)), y(n+1)=((y(n)/x(n-1)*y(n-1)), Applied Mathematics and Computation, 158:303-305.
  • [4] Elabbasy, E. M., El-Metwally, H., Elsayed, E. M. (2008) On the solutions of a class of difference equations systems. Demonstratio Mathematica, 41 (1):109-122.
  • [5] Elsayed, E. M. (2008) On the solutions of higher order rational system of recursive sequences. Mathematica Balkanica, 21(3-4):287-296.
  • [6] Elsayed, E. M. (2009) Dynamics of a recursive sequence of higher order, Communications on Applied Nonlinear Analysis, 16(2):37-50.
  • [7] Elsayed, E. M. (2010) On the solutions of a rational system of difference equations. Fasciculi Mathematici, 45:25–36.
  • [8] Gurbanlyyev, A. (2016) On a system of difference equations. European Journal of Mathematics and Computer Science, 3(1):1-14.
  • [9] Gurbanlyyev, A., Tutuncu, M. (2016) On the behavior of solutions of the system of rational difference equations, European Journal of Mathematics and Computer Science, 3(1):23-42.
  • [10] Haddad, N., Touafek, N., Rabago, J. F. T. (2018) Well-defined solutions of a system of difference equations, Journal of Applied Mathematics and Computing, 56:439-458.
  • [11] Kulenović M. R. S., Nurkanović, Z. (2005) Global behavior of a three-dimensional linear fractional system of difference equations. Journal of Mathematical Analysis and Applications, 310:673-689.
  • [12] Kurbanli, A. S., Çinar, C., Şimşek, D. (2011) On the periodicity of solutions of the system of rational difference equations x(n+1)=(x(n-1)+y(n))/(y(n)*x(n-1)-1)), y(n+1)=(y(n-1)+x(n))/(x(n)*y(n-1)-1)), Applied Mathematics, 2:410-413.
  • [13] Kurbanli, A. S., Çinar, C., Yalcinkaya, I. (2011) On the behavaior of positive solutions of the system of rational difference equations x(n+1)=(x(n-1)/(y(n)*x(n-1)+1)), y(n+1)=(y(n-1)/(x(n)*y(n-1)+1)), Mathematical and Computer Modelling, 53(5-6):1261-1267.
  • [14] Papaschinopoulos, G., Schinas, C. J. (1998) On a system of two nonlinear difference equations. Journal of Mathematical Analysis and Applications, 219:415-426.
  • [15] Papaschinopoulos, G., Schinas, C. J. (2002) On the system of two difference equations. Journal of Mathematical Analysis and Applications, 273:294-309.
  • [16] Sahinkaya, A. F., Yalcinkaya, I., Tollu, D. T. (2020) A solvable system of nonlinear difference equations. Ikonion Journal of Mathematics, 2(1):10-20.
  • [17] Stević, S., Tollu, D. T. (2019) Solvability of eight classes of nonlinear systems of difference equations. Mathematical Methods in the Applied Sciences, 42:4065-4112.
  • [18] Stević, S., Tollu, D. T. (2019) Solvability and semi-cycle analysis of a class of nonlinear systems of difference equations. Mathematical Methods in the Applied Sciences, 42:3579-3615.
  • [19] Taskara, N., Tollu, D. T., Touafek, N., Yazlik, Y. (2020) A solvable system of difference equations. Communications of the Korean Mathematical Society, 35(1):301-319.
  • [20] Tollu, D. T., Yalçınkaya, I. (2019): 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, 68(1):1-16.
  • [21] Yalcinkaya, I., Çinar, C., Simsek, D. (2008) Global asymptotic stability of a system of difference equations. Applicable Analysis, 87(6):689-699.
  • [22] Yalcinkaya, I., Cinar, C. (2010) Global asymptotic stability of two nonlinear difference equations z(n+1)=(t(n)*z(n-1)+a)/(t(n)+z(n-1)), t(n+1)=(z(n)*t(n-1)+a)/(z(n)+t(n-1)), Fasciculi Mathematici, 43:171-180.
  • [23] Yalcinkaya I., Cinar, C. (2011) On the solutions of a systems of difference equations. International Journal of Mathematics & Statistics, 9(A11):62-67.
  • [24] Yazlik, Y., Kara, M. (2019) On a solvable system of difference equations of higher-order with period two coefficients. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 68(2):1675-1693.
Year 2020, Volume: 2 Issue: 2, 1 - 8, 30.10.2020

Abstract

References

  • [1] Akgüneş, N., Kurbanli, A. S. (2014) On the system of rational difference equations x(n)=f((x(n-a(1)), y(n-a(1))), y(n)=g((y(n-a(1)), z(n-a(1))), z(n)=h((z(n-a(1)), x(n-a(1))), Selcuk Journal of Applied Mathematics, 15(1): 8 pages.
  • [2] Camouzis, E., Papaschinopoulos, G. (2004) Global asymptotic behavior of positive solutions of the system of rational difference equations x(n+1)=(1+(x(n)/y(n-m)), y(n+1)=(1+(y(n)/x(n-m)), Applied Mathematics Letters, 17:733-737.
  • [3] Çinar, C. (2004) On the positive solutions of the difference equation system x(n+1)=(1/y(n)), y(n+1)=((y(n)/x(n-1)*y(n-1)), Applied Mathematics and Computation, 158:303-305.
  • [4] Elabbasy, E. M., El-Metwally, H., Elsayed, E. M. (2008) On the solutions of a class of difference equations systems. Demonstratio Mathematica, 41 (1):109-122.
  • [5] Elsayed, E. M. (2008) On the solutions of higher order rational system of recursive sequences. Mathematica Balkanica, 21(3-4):287-296.
  • [6] Elsayed, E. M. (2009) Dynamics of a recursive sequence of higher order, Communications on Applied Nonlinear Analysis, 16(2):37-50.
  • [7] Elsayed, E. M. (2010) On the solutions of a rational system of difference equations. Fasciculi Mathematici, 45:25–36.
  • [8] Gurbanlyyev, A. (2016) On a system of difference equations. European Journal of Mathematics and Computer Science, 3(1):1-14.
  • [9] Gurbanlyyev, A., Tutuncu, M. (2016) On the behavior of solutions of the system of rational difference equations, European Journal of Mathematics and Computer Science, 3(1):23-42.
  • [10] Haddad, N., Touafek, N., Rabago, J. F. T. (2018) Well-defined solutions of a system of difference equations, Journal of Applied Mathematics and Computing, 56:439-458.
  • [11] Kulenović M. R. S., Nurkanović, Z. (2005) Global behavior of a three-dimensional linear fractional system of difference equations. Journal of Mathematical Analysis and Applications, 310:673-689.
  • [12] Kurbanli, A. S., Çinar, C., Şimşek, D. (2011) On the periodicity of solutions of the system of rational difference equations x(n+1)=(x(n-1)+y(n))/(y(n)*x(n-1)-1)), y(n+1)=(y(n-1)+x(n))/(x(n)*y(n-1)-1)), Applied Mathematics, 2:410-413.
  • [13] Kurbanli, A. S., Çinar, C., Yalcinkaya, I. (2011) On the behavaior of positive solutions of the system of rational difference equations x(n+1)=(x(n-1)/(y(n)*x(n-1)+1)), y(n+1)=(y(n-1)/(x(n)*y(n-1)+1)), Mathematical and Computer Modelling, 53(5-6):1261-1267.
  • [14] Papaschinopoulos, G., Schinas, C. J. (1998) On a system of two nonlinear difference equations. Journal of Mathematical Analysis and Applications, 219:415-426.
  • [15] Papaschinopoulos, G., Schinas, C. J. (2002) On the system of two difference equations. Journal of Mathematical Analysis and Applications, 273:294-309.
  • [16] Sahinkaya, A. F., Yalcinkaya, I., Tollu, D. T. (2020) A solvable system of nonlinear difference equations. Ikonion Journal of Mathematics, 2(1):10-20.
  • [17] Stević, S., Tollu, D. T. (2019) Solvability of eight classes of nonlinear systems of difference equations. Mathematical Methods in the Applied Sciences, 42:4065-4112.
  • [18] Stević, S., Tollu, D. T. (2019) Solvability and semi-cycle analysis of a class of nonlinear systems of difference equations. Mathematical Methods in the Applied Sciences, 42:3579-3615.
  • [19] Taskara, N., Tollu, D. T., Touafek, N., Yazlik, Y. (2020) A solvable system of difference equations. Communications of the Korean Mathematical Society, 35(1):301-319.
  • [20] Tollu, D. T., Yalçınkaya, I. (2019): 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, 68(1):1-16.
  • [21] Yalcinkaya, I., Çinar, C., Simsek, D. (2008) Global asymptotic stability of a system of difference equations. Applicable Analysis, 87(6):689-699.
  • [22] Yalcinkaya, I., Cinar, C. (2010) Global asymptotic stability of two nonlinear difference equations z(n+1)=(t(n)*z(n-1)+a)/(t(n)+z(n-1)), t(n+1)=(z(n)*t(n-1)+a)/(z(n)+t(n-1)), Fasciculi Mathematici, 43:171-180.
  • [23] Yalcinkaya I., Cinar, C. (2011) On the solutions of a systems of difference equations. International Journal of Mathematics & Statistics, 9(A11):62-67.
  • [24] Yazlik, Y., Kara, M. (2019) On a solvable system of difference equations of higher-order with period two coefficients. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 68(2):1675-1693.
There are 24 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Kabul edilmiş makaleler
Authors

Abdullah Kurbanlı

Çağla Yalçınkaya This is me

Publication Date October 30, 2020
Acceptance Date October 16, 2020
Published in Issue Year 2020 Volume: 2 Issue: 2

Cite

APA Kurbanlı, A., & Yalçınkaya, Ç. (2020). ON THE PERIODICITY OF SOLUTIONS OF A SYSTEM OF RATIONAL DIFFERENCE EQUATIONS. Ikonion Journal of Mathematics, 2(2), 1-8.
AMA Kurbanlı A, Yalçınkaya Ç. ON THE PERIODICITY OF SOLUTIONS OF A SYSTEM OF RATIONAL DIFFERENCE EQUATIONS. ikjm. October 2020;2(2):1-8.
Chicago Kurbanlı, Abdullah, and Çağla Yalçınkaya. “ON THE PERIODICITY OF SOLUTIONS OF A SYSTEM OF RATIONAL DIFFERENCE EQUATIONS”. Ikonion Journal of Mathematics 2, no. 2 (October 2020): 1-8.
EndNote Kurbanlı A, Yalçınkaya Ç (October 1, 2020) ON THE PERIODICITY OF SOLUTIONS OF A SYSTEM OF RATIONAL DIFFERENCE EQUATIONS. Ikonion Journal of Mathematics 2 2 1–8.
IEEE A. Kurbanlı and Ç. Yalçınkaya, “ON THE PERIODICITY OF SOLUTIONS OF A SYSTEM OF RATIONAL DIFFERENCE EQUATIONS”, ikjm, vol. 2, no. 2, pp. 1–8, 2020.
ISNAD Kurbanlı, Abdullah - Yalçınkaya, Çağla. “ON THE PERIODICITY OF SOLUTIONS OF A SYSTEM OF RATIONAL DIFFERENCE EQUATIONS”. Ikonion Journal of Mathematics 2/2 (October 2020), 1-8.
JAMA Kurbanlı A, Yalçınkaya Ç. ON THE PERIODICITY OF SOLUTIONS OF A SYSTEM OF RATIONAL DIFFERENCE EQUATIONS. ikjm. 2020;2:1–8.
MLA Kurbanlı, Abdullah and Çağla Yalçınkaya. “ON THE PERIODICITY OF SOLUTIONS OF A SYSTEM OF RATIONAL DIFFERENCE EQUATIONS”. Ikonion Journal of Mathematics, vol. 2, no. 2, 2020, pp. 1-8.
Vancouver Kurbanlı A, Yalçınkaya Ç. ON THE PERIODICITY OF SOLUTIONS OF A SYSTEM OF RATIONAL DIFFERENCE EQUATIONS. ikjm. 2020;2(2):1-8.