Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2019 / Volume: 68 Issue: 2

On a solvable system of difference equations of higher-order with period two coefficients

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Publication Date
2019-08-01
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We show that the next difference equations system

📌 3 Key Takeaways

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Objective & Hypothesis:We show that the next difference equations system
📊
Key Findings & Data:We show that the next difference equations system
💡
Conclusion & Impact:We show that the next difference equations system
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Periodic solution · solution in closed form system of difference equations

Abstract

We show that the next difference equations system

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Cite This Article

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, Volume: 68 Issue: 2. https://doi.org/10.31801/cfsuasmas.548262

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References (40)

  1. Belhannache, F., Touafek, N. and Abo-Zeid, R., On a higher order rational difference equations, Journal of Applied Mathematics and Informatics, 34(5-6), (2016), 369--382.
  2. Dekkar, I., Touafek, N. and Yazlik, Y., 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, 111, (2017), 325--347.
  3. Elabbasy, E. M., El-Metwally, H. and Elsayed, E. M., Qualitative behavior of higher order difference equation, Soochow J. Math, 33, (2007), 861--873.
  4. Cinar, C., Toufik, M. and Yalcinkaya, I., On the difference equation of higher order, Utilitas Mathematica, 92, (2013), 161--166.
  5. Cinar, C., On the positive solutions of the difference equation x_{n+1}=((x_{n-1})/(1+x_{n}x_{n-1})), Applied Mathematics and Computation, 150(1), (2004), 21--24.
  6. Elaydi, S., An Introduction to Difference Equations, Springer, New York, 1996.
  7. El-Dessoky, M. M., The form of solutions and periodicity for some systems of third-order rational difference equations, Mathematical Methods in the Applied Sciences, 39(5), (2016), 1076--1092.
  8. Elsayed, E. M. and Ahmed, A. M., Dynamics of a three dimensional system of rational difference equations, Mathematical Methods in the Applied Sciences, 39(5), (2016), 1026--1038.
  9. Elsayed, E. M., Alotaibi, A. and Almaylabi, H. A., On a solutions of fourth order rational systems of difference equations, Journal of Computational Analysis and Applications, 22(7), (2017), 1298-1308.
  10. Elsayed, E. M., On the solutions and periodic nature of some systems of difference equations, International Journal of Biomathematics, 7(6), (2014), 1--26.
  11. Gelisken, A. and Kara, M., Some general systems of rational difference equations, Journal of Difference Equations, 396757,(2015), 1--7.
  12. Grove, E. A. and Ladas, G., Periodicities in nonlinear difference equations, Advances in Discrete Mathematics and Applications, vol. 4. Chapman & Hall/CRC, London, 2005.
  13. Haddad, N., Touafek, N. and Rabago, J. F. T., Well-defined solutions of a system of difference equations, Journal of Appl. Math. and Comput., DOI: 10.1007/s12190-017-1081-8, (2017), 1--20.
  14. Haddad, N., Touafek, N. and Rabago, J.F.T., Solution form of a higher-order system of difference equations and dynamical behavior of its special case, Mathematical Methods in the Applied Science, 40(10), (2017), 3599--3607.
  15. Halim, Y., Touafek, N. and Yazlik, Y., Dynamic behavior of a second-order nonlinear rational difference equation, Turk. J. Math, 39(6), (2015), 1004--1018.
  16. Ibrahim, T.F. and Touafek, N., On a third order rational difference equation with variable coefficients, Dynamics of Continuous Discrete and Impulsive Systems Series B, 20, (2013), 251--264.
  17. Kulenovic, M. R. S. and Ladas, G., Dynamics of Second Order Rational Difference Equations with Open Problems and Conjectures. Chapman & Hall, CRC Press, London, 2001.
  18. Psarros, N., Papaschinopoulos, G. and Schinas, C.J., Semistability of two systems of difference equations using centre manifold theory, Mathematical Methods in the Applied Sciences, 39(18), (2016), 5216--5222.
  19. Rabago, J.F.T. and Bacani, J.B., On a nonlinear difference equations, Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis, 24, (2017), 375--394.
  20. Stević, S., More on a rational recurrence relation, Appl. Math, E-Notes 4, (2004), 80--85.
  21. Stević, S., On a system of difference equations with period two coefficients, Applied Mathematics and Computation, 218, (2011), 4317--4324.
  22. Stević, S., On the difference equation x_{n}=((x_{n-2})/(b_{n}+c_{n}x_{n}x_{n-2})), Appl. Math. Comput., 218, (2011), 4507--4513.
  23. Stević, S., On a solvable rational system of difference equations, Appl. Math. Comput. 219, (2012), 2896--2908.
  24. Stević, S., Representation of solutions of bilinear difference equations in terms of generalized Fibonacci sequences, Electronic Journal of Qualitative Theory of Differantial Equations, (67), (2014), 1--15.
  25. Stević, S., Alghamdi, M. A., Shahzad, N. and Maturi, D. A., On a class of solvable difference equations, Abstract and Applied Analysis, (2013), Article ID: 157-943, 7 pages.
  26. Stević, S., On a solvable system of difference equations of kth order, Appl. Math. Comput., 219, (2013), 7765--7771.
  27. Stević, S., Diblik, J., Iricanin, B. and Smarda, Z., On a solvable system of rational difference equations, Journal of Difference Equations and Applications, 20(5-6), (2014), 811--825.
  28. 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.
  29. Tollu, D. T., Yazlik, Y. and Taskara, N., On fourteen solvable systems of difference equations, Applied Mathematics and Computation, 233, (2014), 310--319.
  30. Tollu, D. T., Yazlik, Y. and Taskara, N., Behavior of positive solutions of a difference equation, Journal of Applied Mathematics and Informatics, 35, (2017), 217--230.
  31. 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), 1-7.
  32. Tollu D. T., Yazlik Y. and Taskara N., On a solvable nonlinear difference equation of higher-order, Turkish Journal of Mathematics, 42(4), (2018), 1765-1778.
  33. Tollu, D. T. and Yalcinkaya, I., Global behavior of a three-dimensional system of difference equations of order three, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68(1), (2019), 1--16.
  34. Touafek, N., On a second order rational difference equation, Hacet. J. Math. Stat., 41, (2012), 867--874.
  35. Yalcinkaya, I., Hamza, A. E. and Cinar, C., Global behavior of a recursive sequence, Selçuk Journal of Applied Mathematics, 14(1), (2013), 3--10.
  36. Yalcinkaya, I. and Tollu, D. T., Global behavior of a second order system of difference equations, Advanced Studies in Contemporary Mathematics, 26(4), (2016), 653--667.
  37. Yazlik, Y., On the solutions and behavior of rational difference equations, J. Comput. Anal. Appl., 17(3), (2014), 584--594.
  38. Yazlik, Y., Elsayed, E. M. and Taskara, N., On the behaviour of the solutions the solutions of difference equation system, J. Comput. Anal. Appl., 16(5), (2014), 932--941.
  39. Yazlik, Y., Tollu, D. T. and Taskara, N., On the behaviour of solutions for some systems of difference equations, J. Comput. Anal. Appl., 18(1), (2015), 166--178.
  40. 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), (2015), 95--111.