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.
[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.
[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.
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.