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Year 2018, Volume 5, Issue 2, 119 - 123, 29.06.2018
https://doi.org/10.17350/HJSE19030000082

Abstract

References

  • 1. R. Abu-Saris, C. Cinar and I. Yalcinkaya, On the asymptotic stability of , Computers & Mathematics with Applications, 56(5) (2008), 1172-1175.
  • 2. I. Dekkar, N. Touafek and Y. Yazlik, Global stability of a third-order nonlinear system of difference equations with period-two coefficients, Revista de la real academia de ciencias exactas, físicas y naturales. Serie A. Matemáticas, Doi:10.1007/s13398-016-0297-z.
  • 3. E.M. Elsayed, Qualitative behavior of a rational recursive sequence, Indagationes Mathematicae 19(2)(2008), 189- 201.
  • 4. E.M. Elsayed, Qualitative properties for a fourth order rational difference equation, Acta Applicandae Mathematicae 110(2)(2010), 589-604.
  • 5. N. Haddad, N. Touafek and J. F. T. Rabago, Solution form of a higher-order system of difference equations and dynamical behavior of its special case, Mathematical Methods in the Applied Sciences, (2016), doi: 10.1002/mma.4248.
  • 6. N. Haddad, N. Touafek and J. F. T. Rabago, Well-defined solutions of a system of difference equations, Journal of Applied Mathematics and Computing, (2017), Doi:10.1007/ s12190-017-1081-8.
  • 7. Y. Halim, N. Touafek and Y. Yazlik, Dynamic behavior of a second-order nonlinear rational difference equation, Turkish Journal of Mathematics 39(6)(2015), 1004-1018.
  • 8. A. S. Kurbanli, C. Çinar and D. Şimşek, On the periodicity of solutions of the system of rational difference equations, Applied Mathematics, 2 (2011), 410-413.
  • 9. S. Stevic, On some solvable systems of difference equations, Applied Mathematics and Computation, 218 (2012) 5010- 5018.
  • 10. S. Stevic, M. A. Alghamdi, N. Shahzad and D. A. Maturi, On a class of solvable difference equations, Abstract and Applied Analysis, Vol. 2013, Article ID 157943, 7 pages.
  • 11. S. Stevic, Representation of solutions of bilinear difference equations in terms of generalized Fibonacci sequences, Electronic Journal of Qualitative Theory of Differential Equations, 2014, No. 67, (2014), 1-15.
  • 12. S. Stevic, J. Diblík, B. Iricanin and Z. Šmarda, On a solvable system of rational difference equations, Journal of Difference Equations and Applications, 20(5-6)(2014): 811-825.
  • 13. S. Stevic, M. A. Alghamdi, A. Alotaibi and E. M. Elsayed, Solvable product-type system of difference equations of second order, Electronic Journal of Differential Equations, 2015, No:169, (2015), 1-20.
  • 14. S. Stevic, New class of solvable systems of difference equations, Applied Mathematics Letters, 63(2017), 137- 144.
  • 15. N. Taskara, K. Uslu and D. T. Tollu, The periodicity and solutions of the rational difference equation with periodic coefficients, Computers & Mathematics with Applications, 62 (2011), 1807-1813.
  • 16. D. T. Tollu, Y. Yazlik and N. Taskara, On the solutions of two special types of Riccati difference equation via Fibonacci numbers, Advances in Difference Equations, 2013, 2013:174.
  • 17. D. T. Tollu, Y. Yazlik and N. Taskara, On fourteen solvable systems of difference equations, Applied Mathematics and Computation, 233 (2014), 310-319.
  • 18. N. Touafek, On a second order rational difference equation, Hacettepe Journal of Mathematics and Statistics, 41(6) (2012), 867-874.
  • 19. I. Yalcinkaya, C. Cinar and D. Simsek, Global asymptotic stability of a system of difference equations, Applicable Analysis, 87(6)(2008), 677-687, DOI: 10.1080/00036810802140657.
  • 20. I. Yalcinkaya, On the global asymptotic stability of a secondorder system of difference equations, Discrete Dynamics in Nature and Society, vol. 2008, Article ID 860152, 12 pages, 2008. doi:10.1155/2008/860152.
  • 21. I. Yalcinkaya, On the global asymptotic behavior of a system of two nonlinear difference equations, Ars Combinatoria, 95 (2010), 151-159.
  • 22. I. Yalcinkaya and C. Cinar, Global asymptotic stability of two nonlinear difference equations , Fasciculi Mathematici, 43 (2010), 171-180.
  • 23. I. Yalcinkaya and D. T. Tollu, Global behavior of a secondorder system of difference equations, Advanced Studies in Contemporary Mathematics, 26(4)(2016), 653-667.
  • 24. Y. Yazlik, On the solutions and behavior of rational difference equations, Journal of Computational Analysis & Applications, 17(3)(2014), 584-594.
  • 25. Y. Yazlik, E. M. Elsayed and N. Taskara, On the behaviour of the solutions of difference equation systems, Journal of Computational Analysis & Applications, 16(5)(2014), 932- 941.
  • 26. Y. Yazlik, D. T. Tollu and N. Taskara, On the behaviour of solutions for some systems of difference equations, Journal of Computational Analysis & Applications, 18(1)(2015), 166-178.
  • 27. Y. Yazlik, D. T. Tollu and N. Taskara, On the solutions of a max-type difference equation system, Mathematical Methods in the Applied Sciences, 38(17)(2015), 4388-4410.
  • 28. Y. Yazlik, D. T. Tollu and N. Taskara, On the solutions of a three-dimensional system of difference equations, Kuwait Journal of Science 43(1)(2016), 95-111.
  • 29. L. Xianyi and Z. Deming, Global asymptotic stability in a rational equation, Journal of Difference Equations and Applications, 9(9)(2003), 833-839.
  • 30. L. Xianyi and Z. Deming, Two rational recursive sequences, Computers & Mathematics with Applications, 47 (2004) 1487-1494.
  • 31. X. Wang and Z. Li, Global asymptotic stability for two kinds of higher order recursive sequences, Journal of Difference Equations and Applications, 22(10)(2016), 1542-1553, DOI: 10.1080/10236198.2016.1216111.

Explicit Solutions of a Three-dimensional System of Nonlinear Difference Equations

Year 2018, Volume 5, Issue 2, 119 - 123, 29.06.2018
https://doi.org/10.17350/HJSE19030000082

Abstract

I n this paper, we show that the system of difference equations 1 11 0 , , , N , 111 n n nn nn n nn n n n n n n xy yz zx xyz n xy yz zx + ++ + ++ = = = ∈ +++ where the initial values xyz , , are real numbers, are solvable in explicit form via some changes of variables and tricks. Also, we determine the forbidden set of the initial values xyz , , for the above mentioned system and investigate asymptotic behavior of the well-defined solutions by using these explicit formulas

References

  • 1. R. Abu-Saris, C. Cinar and I. Yalcinkaya, On the asymptotic stability of , Computers & Mathematics with Applications, 56(5) (2008), 1172-1175.
  • 2. I. Dekkar, N. Touafek and Y. Yazlik, Global stability of a third-order nonlinear system of difference equations with period-two coefficients, Revista de la real academia de ciencias exactas, físicas y naturales. Serie A. Matemáticas, Doi:10.1007/s13398-016-0297-z.
  • 3. E.M. Elsayed, Qualitative behavior of a rational recursive sequence, Indagationes Mathematicae 19(2)(2008), 189- 201.
  • 4. E.M. Elsayed, Qualitative properties for a fourth order rational difference equation, Acta Applicandae Mathematicae 110(2)(2010), 589-604.
  • 5. N. Haddad, N. Touafek and J. F. T. Rabago, Solution form of a higher-order system of difference equations and dynamical behavior of its special case, Mathematical Methods in the Applied Sciences, (2016), doi: 10.1002/mma.4248.
  • 6. N. Haddad, N. Touafek and J. F. T. Rabago, Well-defined solutions of a system of difference equations, Journal of Applied Mathematics and Computing, (2017), Doi:10.1007/ s12190-017-1081-8.
  • 7. Y. Halim, N. Touafek and Y. Yazlik, Dynamic behavior of a second-order nonlinear rational difference equation, Turkish Journal of Mathematics 39(6)(2015), 1004-1018.
  • 8. A. S. Kurbanli, C. Çinar and D. Şimşek, On the periodicity of solutions of the system of rational difference equations, Applied Mathematics, 2 (2011), 410-413.
  • 9. S. Stevic, On some solvable systems of difference equations, Applied Mathematics and Computation, 218 (2012) 5010- 5018.
  • 10. S. Stevic, M. A. Alghamdi, N. Shahzad and D. A. Maturi, On a class of solvable difference equations, Abstract and Applied Analysis, Vol. 2013, Article ID 157943, 7 pages.
  • 11. S. Stevic, Representation of solutions of bilinear difference equations in terms of generalized Fibonacci sequences, Electronic Journal of Qualitative Theory of Differential Equations, 2014, No. 67, (2014), 1-15.
  • 12. S. Stevic, J. Diblík, B. Iricanin and Z. Šmarda, On a solvable system of rational difference equations, Journal of Difference Equations and Applications, 20(5-6)(2014): 811-825.
  • 13. S. Stevic, M. A. Alghamdi, A. Alotaibi and E. M. Elsayed, Solvable product-type system of difference equations of second order, Electronic Journal of Differential Equations, 2015, No:169, (2015), 1-20.
  • 14. S. Stevic, New class of solvable systems of difference equations, Applied Mathematics Letters, 63(2017), 137- 144.
  • 15. N. Taskara, K. Uslu and D. T. Tollu, The periodicity and solutions of the rational difference equation with periodic coefficients, Computers & Mathematics with Applications, 62 (2011), 1807-1813.
  • 16. D. T. Tollu, Y. Yazlik and N. Taskara, On the solutions of two special types of Riccati difference equation via Fibonacci numbers, Advances in Difference Equations, 2013, 2013:174.
  • 17. D. T. Tollu, Y. Yazlik and N. Taskara, On fourteen solvable systems of difference equations, Applied Mathematics and Computation, 233 (2014), 310-319.
  • 18. N. Touafek, On a second order rational difference equation, Hacettepe Journal of Mathematics and Statistics, 41(6) (2012), 867-874.
  • 19. I. Yalcinkaya, C. Cinar and D. Simsek, Global asymptotic stability of a system of difference equations, Applicable Analysis, 87(6)(2008), 677-687, DOI: 10.1080/00036810802140657.
  • 20. I. Yalcinkaya, On the global asymptotic stability of a secondorder system of difference equations, Discrete Dynamics in Nature and Society, vol. 2008, Article ID 860152, 12 pages, 2008. doi:10.1155/2008/860152.
  • 21. I. Yalcinkaya, On the global asymptotic behavior of a system of two nonlinear difference equations, Ars Combinatoria, 95 (2010), 151-159.
  • 22. I. Yalcinkaya and C. Cinar, Global asymptotic stability of two nonlinear difference equations , Fasciculi Mathematici, 43 (2010), 171-180.
  • 23. I. Yalcinkaya and D. T. Tollu, Global behavior of a secondorder system of difference equations, Advanced Studies in Contemporary Mathematics, 26(4)(2016), 653-667.
  • 24. Y. Yazlik, On the solutions and behavior of rational difference equations, Journal of Computational Analysis & Applications, 17(3)(2014), 584-594.
  • 25. Y. Yazlik, E. M. Elsayed and N. Taskara, On the behaviour of the solutions of difference equation systems, Journal of Computational Analysis & Applications, 16(5)(2014), 932- 941.
  • 26. Y. Yazlik, D. T. Tollu and N. Taskara, On the behaviour of solutions for some systems of difference equations, Journal of Computational Analysis & Applications, 18(1)(2015), 166-178.
  • 27. Y. Yazlik, D. T. Tollu and N. Taskara, On the solutions of a max-type difference equation system, Mathematical Methods in the Applied Sciences, 38(17)(2015), 4388-4410.
  • 28. Y. Yazlik, D. T. Tollu and N. Taskara, On the solutions of a three-dimensional system of difference equations, Kuwait Journal of Science 43(1)(2016), 95-111.
  • 29. L. Xianyi and Z. Deming, Global asymptotic stability in a rational equation, Journal of Difference Equations and Applications, 9(9)(2003), 833-839.
  • 30. L. Xianyi and Z. Deming, Two rational recursive sequences, Computers & Mathematics with Applications, 47 (2004) 1487-1494.
  • 31. X. Wang and Z. Li, Global asymptotic stability for two kinds of higher order recursive sequences, Journal of Difference Equations and Applications, 22(10)(2016), 1542-1553, DOI: 10.1080/10236198.2016.1216111.

Details

Primary Language English
Journal Section Research Article
Authors

Bahriye YİLMAZYİLDİRİM This is me
Necmettin Erbakan University Graduate School of Natural and Applied Science, Turkey


Durhasan Turgut TOLLU This is me
Necmettin Erbakan University, Department of Mathematics-Computer Sciences, Konya, Turkey

Publication Date June 29, 2018
Application Date
Acceptance Date
Published in Issue Year 2018, Volume 5, Issue 2

Cite

Bibtex @ { hjse859934, journal = {Hittite Journal of Science and Engineering}, eissn = {2148-4171}, address = {Hitit Üniversitesi Mühendislik Fakültesi Kuzey Kampüsü Çevre Yolu Bulvarı 19030 Çorum / TÜRKİYE}, publisher = {Hitit University}, year = {2018}, volume = {5}, number = {2}, pages = {119 - 123}, doi = {10.17350/HJSE19030000082}, title = {Explicit Solutions of a Three-dimensional System of Nonlinear Difference Equations}, key = {cite}, author = {Yilmazyildirim, Bahriye and Tollu, Durhasan Turgut} }
APA Yilmazyildirim, B. & Tollu, D. T. (2018). Explicit Solutions of a Three-dimensional System of Nonlinear Difference Equations . Hittite Journal of Science and Engineering , 5 (2) , 119-123 . DOI: 10.17350/HJSE19030000082
MLA Yilmazyildirim, B. , Tollu, D. T. "Explicit Solutions of a Three-dimensional System of Nonlinear Difference Equations" . Hittite Journal of Science and Engineering 5 (2018 ): 119-123 <https://dergipark.org.tr/en/pub/hjse/issue/59663/859934>
Chicago Yilmazyildirim, B. , Tollu, D. T. "Explicit Solutions of a Three-dimensional System of Nonlinear Difference Equations". Hittite Journal of Science and Engineering 5 (2018 ): 119-123
RIS TY - JOUR T1 - Explicit Solutions of a Three-dimensional System of Nonlinear Difference Equations AU - BahriyeYilmazyildirim, Durhasan TurgutTollu Y1 - 2018 PY - 2018 N1 - doi: 10.17350/HJSE19030000082 DO - 10.17350/HJSE19030000082 T2 - Hittite Journal of Science and Engineering JF - Journal JO - JOR SP - 119 EP - 123 VL - 5 IS - 2 SN - -2148-4171 M3 - doi: 10.17350/HJSE19030000082 UR - https://doi.org/10.17350/HJSE19030000082 Y2 - 2022 ER -
EndNote %0 Hittite Journal of Science and Engineering Explicit Solutions of a Three-dimensional System of Nonlinear Difference Equations %A Bahriye Yilmazyildirim , Durhasan Turgut Tollu %T Explicit Solutions of a Three-dimensional System of Nonlinear Difference Equations %D 2018 %J Hittite Journal of Science and Engineering %P -2148-4171 %V 5 %N 2 %R doi: 10.17350/HJSE19030000082 %U 10.17350/HJSE19030000082
ISNAD Yilmazyildirim, Bahriye , Tollu, Durhasan Turgut . "Explicit Solutions of a Three-dimensional System of Nonlinear Difference Equations". Hittite Journal of Science and Engineering 5 / 2 (June 2018): 119-123 . https://doi.org/10.17350/HJSE19030000082
AMA Yilmazyildirim B. , Tollu D. T. Explicit Solutions of a Three-dimensional System of Nonlinear Difference Equations. Hittite J Sci Eng. 2018; 5(2): 119-123.
Vancouver Yilmazyildirim B. , Tollu D. T. Explicit Solutions of a Three-dimensional System of Nonlinear Difference Equations. Hittite Journal of Science and Engineering. 2018; 5(2): 119-123.
IEEE B. Yilmazyildirim and D. T. Tollu , "Explicit Solutions of a Three-dimensional System of Nonlinear Difference Equations", Hittite Journal of Science and Engineering, vol. 5, no. 2, pp. 119-123, Jun. 2018, doi:10.17350/HJSE19030000082