Research Article
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Year 2019, Volume: 2 Issue: 3, 116 - 125, 30.09.2019
https://doi.org/10.32323/ujma.589274

Abstract

References

  • [1] M.R.S. Kulenovic, G. Ladas, Dynamics of Second Order Rational Difference Equations. Chapman & Hall/CRC, Boca Raton, London, (2001).
  • [2] D.T. Tollu, Y. Yazlık, N. Tas¸kara, On the solutions of two special types of Riccati difference equation via Fibonacci numbers, Adv. Differ. Equ., 2013 (2013), 174.
  • [3] Y. Yazlık, D.T. Tollu, N. Taskara, On the Solutions of Difference Equation Systems with Padovan Numbers, Appl. Math., 4 (2013), 15-20.
  • [4] D.T. Tollu, Y. Yazlık, N. Taskara, On fourteen solvable systems of difference equations, Appl. Math. Comp., 233 (2014), 310-319.
  • [5] Y. Halim, Global Character of Systems of Rational Difference Equations, Elect. J. Mathe. Anal. Appl., 3(1) (2015), 204-214.
  • [6] Y. Halim, M. Bayram, On the solutions of a higher-order difference equation in terms of generalized Fibonacci sequences, Mathe. Meth. Appl. Sci., 39 (2016), 2974-2982.
  • [7] Y. Halim, A System of Difference Equations with Solutions Associated to Fibonacci Numbers, Int. J. Differ. Equ., 11(1) (2016), 65-77.
  • [8] Y. Halim, J.F.T. Rabago, On the Some Solvable Systems of Difference Equations with Solutions Associated to Fibonacci Numbers, Elect. J. Mathe. Anal. Appl., 5(1) (2017), 166-178.
  • [9] Y. Halim, J.F.T. Rabago, On the Solutions of a Second-Order Difference Equation in terms of Generalized Padovan Sequences, Mathe. Slovaca, 68(3) (2018), 625-638.
  • [10] ˙I. Okumus¸, Y. Soykan, Dynamical Behavior of a System of Three-Dimensional Nonlinear Difference Equations, Adv. Differ. Equ., 2018 (2018), 223.
  • [11] ˙I. Okumus¸, Y. Soykan, On the Dynamics of a Higher Order Nonlinear System of Difference Equations, arXiv:1810.07986v1 [math.DS], 2018.
  • [12] H. Matsunaga, R. Suzuki, Classification of global behavior of a system of rational difference equations, Appl. Math. Lett. 85 (2018), 57-63.
  • [13] M. Göcen, A. Cebeci, On the Periodic Solutions of Some Systems of Higher Order Difference Equations, Rocky Mountain J. Math., 48(3) (2018), 845-858.
  • [14] M. Göcen, M. Güneysu, The Global Attractivity of Some Rational Difference Equations, J. Comput. Anal. Appl., 25(7) (2018), 1233-1243.
  • [15] E. Tas¸demir, Y. Soykan, Dynamical Analysis of a Non-Linear Difference Equation, J. Comput. Anal. Appl., 26(2) (2019), 288-301.
  • [16] E. Tas¸demir, On The Dynamics of a Nonlinear Difference Equation, Adıyaman Uni. J. Sci., 9 (1) (2019), 190-201.
  • [17] İ. Okumus¸, Y. Soykan, On the Solutions of Systems of Difference Equations via Tribonacci Numbers, arXiv:1906.09987v1 [math.DS], 2019.
  • [18] İ. Okumus¸, Y. Soykan, On the Solutions of Four Rational Difference Equations Associated to Tribonacci Numbers, preprints201906.0266.v1, 2019.
  • [19] İ. Okumus¸, Y. Soykan, On the Dynamics of Solutions of a Rational Difference Equation via Generalized Tribonacci Numbers, arXiv:1906.11629v1 [math.DS], 2019.
  • [20] Ö. Öcalan, O. Duman, On Solutions of the Recursive Equations $x_{n+1}=x_{n-1}^{p}/x_{n}^{p}$ $p>0$ via Fibonacci-Type Sequences, Elect. J. Mathe. Anal. Appl., 7(1) (2019), 102-115.

On the Solutions of Four Second-Order Nonlinear Difference Equations

Year 2019, Volume: 2 Issue: 3, 116 - 125, 30.09.2019
https://doi.org/10.32323/ujma.589274

Abstract

This paper deals with the form, the stability character, the periodicity and the global behavior of solutions of the following four rational difference equations \[x_{n+1} &=\frac{\pm 1}{x_{n}\left( x_{n-1}\pm 1\right) -1} \\ x_{n+1} &=\frac{\pm 1}{x_{n}\left( x_{n-1}\mp 1\right) +1}\text{.} \]. 

References

  • [1] M.R.S. Kulenovic, G. Ladas, Dynamics of Second Order Rational Difference Equations. Chapman & Hall/CRC, Boca Raton, London, (2001).
  • [2] D.T. Tollu, Y. Yazlık, N. Tas¸kara, On the solutions of two special types of Riccati difference equation via Fibonacci numbers, Adv. Differ. Equ., 2013 (2013), 174.
  • [3] Y. Yazlık, D.T. Tollu, N. Taskara, On the Solutions of Difference Equation Systems with Padovan Numbers, Appl. Math., 4 (2013), 15-20.
  • [4] D.T. Tollu, Y. Yazlık, N. Taskara, On fourteen solvable systems of difference equations, Appl. Math. Comp., 233 (2014), 310-319.
  • [5] Y. Halim, Global Character of Systems of Rational Difference Equations, Elect. J. Mathe. Anal. Appl., 3(1) (2015), 204-214.
  • [6] Y. Halim, M. Bayram, On the solutions of a higher-order difference equation in terms of generalized Fibonacci sequences, Mathe. Meth. Appl. Sci., 39 (2016), 2974-2982.
  • [7] Y. Halim, A System of Difference Equations with Solutions Associated to Fibonacci Numbers, Int. J. Differ. Equ., 11(1) (2016), 65-77.
  • [8] Y. Halim, J.F.T. Rabago, On the Some Solvable Systems of Difference Equations with Solutions Associated to Fibonacci Numbers, Elect. J. Mathe. Anal. Appl., 5(1) (2017), 166-178.
  • [9] Y. Halim, J.F.T. Rabago, On the Solutions of a Second-Order Difference Equation in terms of Generalized Padovan Sequences, Mathe. Slovaca, 68(3) (2018), 625-638.
  • [10] ˙I. Okumus¸, Y. Soykan, Dynamical Behavior of a System of Three-Dimensional Nonlinear Difference Equations, Adv. Differ. Equ., 2018 (2018), 223.
  • [11] ˙I. Okumus¸, Y. Soykan, On the Dynamics of a Higher Order Nonlinear System of Difference Equations, arXiv:1810.07986v1 [math.DS], 2018.
  • [12] H. Matsunaga, R. Suzuki, Classification of global behavior of a system of rational difference equations, Appl. Math. Lett. 85 (2018), 57-63.
  • [13] M. Göcen, A. Cebeci, On the Periodic Solutions of Some Systems of Higher Order Difference Equations, Rocky Mountain J. Math., 48(3) (2018), 845-858.
  • [14] M. Göcen, M. Güneysu, The Global Attractivity of Some Rational Difference Equations, J. Comput. Anal. Appl., 25(7) (2018), 1233-1243.
  • [15] E. Tas¸demir, Y. Soykan, Dynamical Analysis of a Non-Linear Difference Equation, J. Comput. Anal. Appl., 26(2) (2019), 288-301.
  • [16] E. Tas¸demir, On The Dynamics of a Nonlinear Difference Equation, Adıyaman Uni. J. Sci., 9 (1) (2019), 190-201.
  • [17] İ. Okumus¸, Y. Soykan, On the Solutions of Systems of Difference Equations via Tribonacci Numbers, arXiv:1906.09987v1 [math.DS], 2019.
  • [18] İ. Okumus¸, Y. Soykan, On the Solutions of Four Rational Difference Equations Associated to Tribonacci Numbers, preprints201906.0266.v1, 2019.
  • [19] İ. Okumus¸, Y. Soykan, On the Dynamics of Solutions of a Rational Difference Equation via Generalized Tribonacci Numbers, arXiv:1906.11629v1 [math.DS], 2019.
  • [20] Ö. Öcalan, O. Duman, On Solutions of the Recursive Equations $x_{n+1}=x_{n-1}^{p}/x_{n}^{p}$ $p>0$ via Fibonacci-Type Sequences, Elect. J. Mathe. Anal. Appl., 7(1) (2019), 102-115.
There are 20 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

İnci Okumuş 0000-0003-3711-8144

Yüksel Soykan 0000-0002-1895-211X

Publication Date September 30, 2019
Submission Date July 9, 2019
Acceptance Date September 20, 2019
Published in Issue Year 2019 Volume: 2 Issue: 3

Cite

APA Okumuş, İ., & Soykan, Y. (2019). On the Solutions of Four Second-Order Nonlinear Difference Equations. Universal Journal of Mathematics and Applications, 2(3), 116-125. https://doi.org/10.32323/ujma.589274
AMA Okumuş İ, Soykan Y. On the Solutions of Four Second-Order Nonlinear Difference Equations. Univ. J. Math. Appl. September 2019;2(3):116-125. doi:10.32323/ujma.589274
Chicago Okumuş, İnci, and Yüksel Soykan. “On the Solutions of Four Second-Order Nonlinear Difference Equations”. Universal Journal of Mathematics and Applications 2, no. 3 (September 2019): 116-25. https://doi.org/10.32323/ujma.589274.
EndNote Okumuş İ, Soykan Y (September 1, 2019) On the Solutions of Four Second-Order Nonlinear Difference Equations. Universal Journal of Mathematics and Applications 2 3 116–125.
IEEE İ. Okumuş and Y. Soykan, “On the Solutions of Four Second-Order Nonlinear Difference Equations”, Univ. J. Math. Appl., vol. 2, no. 3, pp. 116–125, 2019, doi: 10.32323/ujma.589274.
ISNAD Okumuş, İnci - Soykan, Yüksel. “On the Solutions of Four Second-Order Nonlinear Difference Equations”. Universal Journal of Mathematics and Applications 2/3 (September 2019), 116-125. https://doi.org/10.32323/ujma.589274.
JAMA Okumuş İ, Soykan Y. On the Solutions of Four Second-Order Nonlinear Difference Equations. Univ. J. Math. Appl. 2019;2:116–125.
MLA Okumuş, İnci and Yüksel Soykan. “On the Solutions of Four Second-Order Nonlinear Difference Equations”. Universal Journal of Mathematics and Applications, vol. 2, no. 3, 2019, pp. 116-25, doi:10.32323/ujma.589274.
Vancouver Okumuş İ, Soykan Y. On the Solutions of Four Second-Order Nonlinear Difference Equations. Univ. J. Math. Appl. 2019;2(3):116-25.

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