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Year 2018, Volume: 5 Issue: 2, 119 - 123, 29.06.2018

Bahriye Yilmazyildirim Durhasan Turgut Tollu

https://doi.org/10.17350/HJSE19030000082
Cited By: 2

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

Bahriye Yilmazyildirim Durhasan Turgut Tollu

https://doi.org/10.17350/HJSE19030000082
Cited By: 2

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

Keywords

Asymptotic behavior explicit solution rational difference equation system

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.
There are 31 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Bahriye Yilmazyildirim This is me

Durhasan Turgut Tollu This is me

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

Cite

Vancouver Yilmazyildirim B, Tollu DT. Explicit Solutions of a Three-dimensional System of Nonlinear Difference Equations. Hittite J Sci Eng. 2018;5(2):119-23.

Cited By

On The Solutions of Three-Dimensional Difference Equation Systems Via Pell Numbers
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https://doi.org/10.31590/ejosat.1082643
On The Solutions of Three-Dimensional Difference Equation Systems Via Pell Numbers
European Journal of Science and Technology
https://doi.org/10.31590/ejosat.1083309
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