Global behavior of a three-dimensional system of difference equations of order three

Durhasan Turgut Tollu; İbrahim Yalçınkaya

doi:10.31801/cfsuasmas.443530

Araştırma Makalesi

Yıl 2019, Cilt: 68 Sayı: 1, 1 - 16, 01.02.2019

Durhasan Turgut Tollu İbrahim Yalçınkaya

https://doi.org/10.31801/cfsuasmas.443530

Cited By: 13

Öz

Kaynakça

Din, Q., Qureshi M. N. and Khan, A. Q., Dynamics of a fourth-order system of rational difference equations, Advances in Difference Equations, (2012), 2012:215.
Din, Q. and Elsayed, E. M., Stability analysis of a discrete ecological model, Computational Ecology and Software, 4(2)(2014), 89-103.
Din, Q., Ibrahim, T. F. and Khan, A. Q., Behavior of a competitive system of second-order difference equations, The Scientific World Journal, vol. 2014, Article ID 283982, 9 pages.
Elabbasy, E. M., El-Metwally, H. and Elsayed, E. M., Some properties and expressions of solutions for a class of nonlinear difference equation, Utilitas Mathematica, 87(2012), 93-110.
El-Metwally, H. and Elsayed, E. M., Solution and behavior of a third rational difference equation, Utilitas Mathematica, 88(2012), 27--42.
El-Metwally, H., Yalcinkaya, I. and Cinar, C., Global stability of an economic model, Utilitas Mathematica, 95(2014), 235-244.
El-Owaidy, H. M., Ahmed, A. M. and Youssef, A. M., The dynamics of the recursive sequence x_{n+1}=((αx_{n-1})/(β+γx_{n-2}^{p})), Applied Mathematics Letters, 18(9)(2005), 1013-1018.
Elaydi, S., An introduction to difference equations, third edition, undergraduate texts in mathematics, Springer, New York, 1999.
Elsayed, E. M., El-Dessoky, M. M. and Alotaibi, A., On the solutions of a general system of difference equations, Discrete Dynamics in Nature and Society, Article ID 892571, (2012).
Gumus, M. and Soykan, Y., Global character of a six dimensional nonlinear system of difference equations, Discrete Dynamics in Nature and Society, vol. 2016, Article ID 6842521, 7 pages.
Kocic, V. L., and Ladas, G., Global behavior of nonlinear difference equations of higher order with applications, Kluwer Academic, Dordrecht, 1993.
Kulenović, M. R. S. and Nurkanović, Z., Global behavior of a three-dimensional linear fractional system of difference equations, Journal of Mathematical Analysis and Applications, 310(2)(2005), 673-689.
Kurbanli, A. S., Cinar, C. and Yalcinkaya, I., On the behavior 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)(2011), 1261-1267.
Kurbanli, A. S., On the behavior of 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), z_{n+1}=1/(y_{n}z_{n}), Advances in Difference Equations, 2011: 40.
Kurbanli, A. S., On the behavior of 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), z_{n+1}=z_{n-1}/(y_{n}z_{n-1}-1), Discrete Dynamics in Nature and Society, vol. 2011, Article ID 932362, 12 pages.
Ozkan, O. and Kurbanli, A. S., On a system of difference equations, Discrete Dynamics in Nature and Society, vol. 2013, Article ID 970316, 7 pages.
Papaschinopoulos, G., Ellina, G. and Papadopoulos, K. B., Asymptotic behavior of the positive solutions of an exponential type system of difference equations, Applied Mathematics and Computation, 245(2014), 181-190
Papaschinopoluos, G., Psarros, N. and Papadopoulos, K. B., On a cyclic system of m difference equations having exponential terms, Electronic Journal of Qualitative Theory of Differential Equations, 5(2015), 1-13.
Taskara, N., Uslu, K. and Tollu, D.T., The periodicity and solutions of the rational difference equation with periodic coefficients, Computers & Mathematics with Applications, 62(2011), 1807-1813.
Taskara, N., Tollu, D. T. and Yazlik, Y., Solutions of rational difference system of order three in terms of Padovan numbers, Journal of Advanced Research in Applied Mathematics, 7(3)(2015), 18-29.
Tollu, D. T., Yazlik Y. and Taskara, N., On the solutions of two special types of Riccati difference equation via Fibonacci numbers, Advances in Difference Equations, 2013:174, (2013).
Tollu, D. T., Yazlik Y. and Taskara, N., On fourteen solvable systems of difference equations, Applied Mathematics and Computation, 233(2014), 310-319.
Tollu, D. T., Yazlik Y. and Taskara, N., The solutions of four Riccati difference equations associated with Fibonacci numbers, Balkan Journal Of Mathematics, 2(2014), 163-172.
Touafek, N. and Elsayed, E. M., On the periodicity of some systems of nonlinear difference equations, Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie, 55(103), No: 2, (2012), 217-224.
Van Khuong, V. and Nam Phong, M., On a system of two difference equations of exponential form, International Journal of Difference Equations, 8(2)(2013), 215-223.
Yalcinkaya, I., Cinar, C. and Simsek, D., Global asymptotic stability of a system of difference equations, Applicable Analysis, 87(6)(2008), 689-699.
Yalcinkaya, I., On the global asymptotic stability of a second-order system of difference equations, Discrete Dynamics in Nature and Society, vol. 2008, Article ID 860152, 12 pages.
Yalcinkaya, I., Cinar, C. and Atalay, M., On the solutions of systems of difference equations, Advances in Difference Equations, 9(2008), Article ID 143943.
Yazlik, Y., Tollu, D. T. and Taskara, N., On the solutions of difference equation systems with Padovan numbers, Applied Mathematics, 4(2013), 15-20.
Yazlik, Y., On the solutions and behavior of rational difference equations, Journal of Computational Analysis and Applications, 17(3)(2014), 584-594.
Yazlik, Y., Elsayed, E. M. and Taskara, N., On the behaviour of the solutions of difference equation systems, Journal of Computational Analysis and Applications, 16(5)(2014), 932-941.
Yazlik, Y., Tollu, D. T. and Taskara, N., On the behaviour of solutions for some systems of difference equations, Journal of Computational Analysis & Applications, 18(1)(2015), 166-178.
Yazlik, Y., Tollu, D. T. and Taskara, N., On the solutions of a max-type difference equation system, Mathematical Methods in the Applied Sciences, 38(17)(2015), 4388--4410.
Yazlik, Y., Tollu, D. T. and Taskara, N., On the solutions of a three-dimensional system of difference equations, Kuwait Journal of Science, 43(1)( 2016), 95-111.

Global behavior of a three-dimensional system of difference equations of order three

Yıl 2019, Cilt: 68 Sayı: 1, 1 - 16, 01.02.2019

Durhasan Turgut Tollu İbrahim Yalçınkaya

https://doi.org/10.31801/cfsuasmas.443530

Cited By: 13

Öz

In this paper, we investigate the global behavior of the positive solutions of the system of difference equations

u_{n+1}=((α₁u_{n-1})/(β₁+γ₁v_{n-2}^{p})), v_{n+1}=((α₂v_{n-1})/(β₂+γ₂w_{n-2}^{q})), w_{n+1}=((α₃w_{n-1})/(β₃+γ₃u_{n-2}^{r}))

for n∈ℕ₀ where the initial conditions u_{-i},v_{-i},w_{-i} (i=0,1,2) are non-negative real numbers and the parameters α_{j},β_{j},γ_{j} (j=1,2,3) and p,q,r are positive real numbers, by extending some results in the literature.

Anahtar Kelimeler

System of difference equations, stability, global behavior, periodic solution

Kaynakça

Din, Q., Qureshi M. N. and Khan, A. Q., Dynamics of a fourth-order system of rational difference equations, Advances in Difference Equations, (2012), 2012:215.
Din, Q. and Elsayed, E. M., Stability analysis of a discrete ecological model, Computational Ecology and Software, 4(2)(2014), 89-103.
Din, Q., Ibrahim, T. F. and Khan, A. Q., Behavior of a competitive system of second-order difference equations, The Scientific World Journal, vol. 2014, Article ID 283982, 9 pages.
Elabbasy, E. M., El-Metwally, H. and Elsayed, E. M., Some properties and expressions of solutions for a class of nonlinear difference equation, Utilitas Mathematica, 87(2012), 93-110.
El-Metwally, H. and Elsayed, E. M., Solution and behavior of a third rational difference equation, Utilitas Mathematica, 88(2012), 27--42.
El-Metwally, H., Yalcinkaya, I. and Cinar, C., Global stability of an economic model, Utilitas Mathematica, 95(2014), 235-244.
El-Owaidy, H. M., Ahmed, A. M. and Youssef, A. M., The dynamics of the recursive sequence x_{n+1}=((αx_{n-1})/(β+γx_{n-2}^{p})), Applied Mathematics Letters, 18(9)(2005), 1013-1018.
Elaydi, S., An introduction to difference equations, third edition, undergraduate texts in mathematics, Springer, New York, 1999.
Elsayed, E. M., El-Dessoky, M. M. and Alotaibi, A., On the solutions of a general system of difference equations, Discrete Dynamics in Nature and Society, Article ID 892571, (2012).
Gumus, M. and Soykan, Y., Global character of a six dimensional nonlinear system of difference equations, Discrete Dynamics in Nature and Society, vol. 2016, Article ID 6842521, 7 pages.
Kocic, V. L., and Ladas, G., Global behavior of nonlinear difference equations of higher order with applications, Kluwer Academic, Dordrecht, 1993.
Kulenović, M. R. S. and Nurkanović, Z., Global behavior of a three-dimensional linear fractional system of difference equations, Journal of Mathematical Analysis and Applications, 310(2)(2005), 673-689.
Kurbanli, A. S., Cinar, C. and Yalcinkaya, I., On the behavior 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)(2011), 1261-1267.
Kurbanli, A. S., On the behavior of 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), z_{n+1}=1/(y_{n}z_{n}), Advances in Difference Equations, 2011: 40.
Kurbanli, A. S., On the behavior of 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), z_{n+1}=z_{n-1}/(y_{n}z_{n-1}-1), Discrete Dynamics in Nature and Society, vol. 2011, Article ID 932362, 12 pages.
Ozkan, O. and Kurbanli, A. S., On a system of difference equations, Discrete Dynamics in Nature and Society, vol. 2013, Article ID 970316, 7 pages.
Papaschinopoulos, G., Ellina, G. and Papadopoulos, K. B., Asymptotic behavior of the positive solutions of an exponential type system of difference equations, Applied Mathematics and Computation, 245(2014), 181-190
Papaschinopoluos, G., Psarros, N. and Papadopoulos, K. B., On a cyclic system of m difference equations having exponential terms, Electronic Journal of Qualitative Theory of Differential Equations, 5(2015), 1-13.
Taskara, N., Uslu, K. and Tollu, D.T., The periodicity and solutions of the rational difference equation with periodic coefficients, Computers & Mathematics with Applications, 62(2011), 1807-1813.
Taskara, N., Tollu, D. T. and Yazlik, Y., Solutions of rational difference system of order three in terms of Padovan numbers, Journal of Advanced Research in Applied Mathematics, 7(3)(2015), 18-29.
Tollu, D. T., Yazlik Y. and Taskara, N., On the solutions of two special types of Riccati difference equation via Fibonacci numbers, Advances in Difference Equations, 2013:174, (2013).
Tollu, D. T., Yazlik Y. and Taskara, N., On fourteen solvable systems of difference equations, Applied Mathematics and Computation, 233(2014), 310-319.
Tollu, D. T., Yazlik Y. and Taskara, N., The solutions of four Riccati difference equations associated with Fibonacci numbers, Balkan Journal Of Mathematics, 2(2014), 163-172.
Touafek, N. and Elsayed, E. M., On the periodicity of some systems of nonlinear difference equations, Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie, 55(103), No: 2, (2012), 217-224.
Van Khuong, V. and Nam Phong, M., On a system of two difference equations of exponential form, International Journal of Difference Equations, 8(2)(2013), 215-223.
Yalcinkaya, I., Cinar, C. and Simsek, D., Global asymptotic stability of a system of difference equations, Applicable Analysis, 87(6)(2008), 689-699.
Yalcinkaya, I., On the global asymptotic stability of a second-order system of difference equations, Discrete Dynamics in Nature and Society, vol. 2008, Article ID 860152, 12 pages.
Yalcinkaya, I., Cinar, C. and Atalay, M., On the solutions of systems of difference equations, Advances in Difference Equations, 9(2008), Article ID 143943.
Yazlik, Y., Tollu, D. T. and Taskara, N., On the solutions of difference equation systems with Padovan numbers, Applied Mathematics, 4(2013), 15-20.
Yazlik, Y., On the solutions and behavior of rational difference equations, Journal of Computational Analysis and Applications, 17(3)(2014), 584-594.
Yazlik, Y., Elsayed, E. M. and Taskara, N., On the behaviour of the solutions of difference equation systems, Journal of Computational Analysis and Applications, 16(5)(2014), 932-941.
Yazlik, Y., Tollu, D. T. and Taskara, N., On the behaviour of solutions for some systems of difference equations, Journal of Computational Analysis & Applications, 18(1)(2015), 166-178.
Yazlik, Y., Tollu, D. T. and Taskara, N., On the solutions of a max-type difference equation system, Mathematical Methods in the Applied Sciences, 38(17)(2015), 4388--4410.
Yazlik, Y., Tollu, D. T. and Taskara, N., On the solutions of a three-dimensional system of difference equations, Kuwait Journal of Science, 43(1)( 2016), 95-111.

Toplam 34 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Konular	Matematik
Bölüm	Makaleler
Yazarlar	Durhasan Turgut Tollu 0000-0002-3313-8829 İbrahim Yalçınkaya 0000-0003-4546-4493
Yayımlanma Tarihi	1 Şubat 2019
Gönderilme Tarihi	1 Ocak 2017
Kabul Tarihi	27 Kasım 2017
Yayımlandığı Sayı	Yıl 2019 Cilt: 68 Sayı: 1

Kaynak Göster

APA	Tollu, D. T., & Yalçınkaya, İ. (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. https://doi.org/10.31801/cfsuasmas.443530
AMA	Tollu DT, Yalçınkaya İ. Global behavior of a three-dimensional system of difference equations of order three. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Şubat 2019;68(1):1-16. doi:10.31801/cfsuasmas.443530
Chicago	Tollu, Durhasan Turgut, ve İbrahim Yalçınkaya. “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, sy. 1 (Şubat 2019): 1-16. https://doi.org/10.31801/cfsuasmas.443530.
EndNote	Tollu DT, Yalçınkaya İ (01 Şubat 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.
IEEE	D. T. Tollu ve İ. Yalçınkaya, “Global behavior of a three-dimensional system of difference equations of order three”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 68, sy. 1, ss. 1–16, 2019, doi: 10.31801/cfsuasmas.443530.
ISNAD	Tollu, Durhasan Turgut - Yalçınkaya, İbrahim. “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 (Şubat 2019), 1-16. https://doi.org/10.31801/cfsuasmas.443530.
JAMA	Tollu DT, Yalçınkaya İ. Global behavior of a three-dimensional system of difference equations of order three. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:1–16.
MLA	Tollu, Durhasan Turgut ve İbrahim Yalçınkaya. “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, c. 68, sy. 1, 2019, ss. 1-16, doi:10.31801/cfsuasmas.443530.
Vancouver	Tollu DT, Yalçınkaya İ. Global behavior of a three-dimensional system of difference equations of order three. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(1):1-16.