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Neimark-Sacker Bifurcation of a Third Order Difference Equation

Year 2019, Volume: 2 Issue: 1, 40 - 49, 17.06.2019
https://doi.org/10.33401/fujma.527572

Abstract

In this paper, we investigate the bifurcation of a third order rational difference equation. Firstly, we show that the equation undergoes a Neimark-Sacker bifurcation when the parameter reaches a critical value. Then, we consider the direction of the Neimark-Sacker bifurcation. Finally, we give some numerical simulations of our results.

References

  • [1] E. Camouzis, Global analysis of solutions of $x_{n+1}=\frac{\beta x_n+\delta x_{n-2}}{A+Bx_n+Cx_{n-1}}$, J. Math Anal. Appl., 316 (2005), 616-627.
  • [2] Z. He, J. Qiu, Neimark-Sacker bifurcation of a third order rational difference equation, J. Differ. Equ. Appl.,19 (2013), 1513-1522.
  • [3] E. Camouzis, G. Ladas, Dynamics of Third-Order Rational Difference Equations with Open Problems and Conjectures, Chapman & Hall/CRC, New York, 2002.
  • [4] A. D. Polyanin, A. I. Chernoutsan, A. Concise, A Concise Handbook of Mathematics, Physics and Engineering Science, CRC Press, New York, 2011.
  • [5] Y. Kuznetsov, Elements of Applied Bifurcation Theory, 2nd edition, Springer, New York, 2003.
Year 2019, Volume: 2 Issue: 1, 40 - 49, 17.06.2019
https://doi.org/10.33401/fujma.527572

Abstract

References

  • [1] E. Camouzis, Global analysis of solutions of $x_{n+1}=\frac{\beta x_n+\delta x_{n-2}}{A+Bx_n+Cx_{n-1}}$, J. Math Anal. Appl., 316 (2005), 616-627.
  • [2] Z. He, J. Qiu, Neimark-Sacker bifurcation of a third order rational difference equation, J. Differ. Equ. Appl.,19 (2013), 1513-1522.
  • [3] E. Camouzis, G. Ladas, Dynamics of Third-Order Rational Difference Equations with Open Problems and Conjectures, Chapman & Hall/CRC, New York, 2002.
  • [4] A. D. Polyanin, A. I. Chernoutsan, A. Concise, A Concise Handbook of Mathematics, Physics and Engineering Science, CRC Press, New York, 2011.
  • [5] Y. Kuznetsov, Elements of Applied Bifurcation Theory, 2nd edition, Springer, New York, 2003.
There are 5 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Marwan Aloqeili 0000-0002-9030-1717

Asmaa Shareef This is me 0000-0001-8109-5811

Publication Date June 17, 2019
Submission Date February 15, 2019
Acceptance Date April 25, 2019
Published in Issue Year 2019 Volume: 2 Issue: 1

Cite

APA Aloqeili, M., & Shareef, A. (2019). Neimark-Sacker Bifurcation of a Third Order Difference Equation. Fundamental Journal of Mathematics and Applications, 2(1), 40-49. https://doi.org/10.33401/fujma.527572
AMA Aloqeili M, Shareef A. Neimark-Sacker Bifurcation of a Third Order Difference Equation. Fundam. J. Math. Appl. June 2019;2(1):40-49. doi:10.33401/fujma.527572
Chicago Aloqeili, Marwan, and Asmaa Shareef. “Neimark-Sacker Bifurcation of a Third Order Difference Equation”. Fundamental Journal of Mathematics and Applications 2, no. 1 (June 2019): 40-49. https://doi.org/10.33401/fujma.527572.
EndNote Aloqeili M, Shareef A (June 1, 2019) Neimark-Sacker Bifurcation of a Third Order Difference Equation. Fundamental Journal of Mathematics and Applications 2 1 40–49.
IEEE M. Aloqeili and A. Shareef, “Neimark-Sacker Bifurcation of a Third Order Difference Equation”, Fundam. J. Math. Appl., vol. 2, no. 1, pp. 40–49, 2019, doi: 10.33401/fujma.527572.
ISNAD Aloqeili, Marwan - Shareef, Asmaa. “Neimark-Sacker Bifurcation of a Third Order Difference Equation”. Fundamental Journal of Mathematics and Applications 2/1 (June 2019), 40-49. https://doi.org/10.33401/fujma.527572.
JAMA Aloqeili M, Shareef A. Neimark-Sacker Bifurcation of a Third Order Difference Equation. Fundam. J. Math. Appl. 2019;2:40–49.
MLA Aloqeili, Marwan and Asmaa Shareef. “Neimark-Sacker Bifurcation of a Third Order Difference Equation”. Fundamental Journal of Mathematics and Applications, vol. 2, no. 1, 2019, pp. 40-49, doi:10.33401/fujma.527572.
Vancouver Aloqeili M, Shareef A. Neimark-Sacker Bifurcation of a Third Order Difference Equation. Fundam. J. Math. Appl. 2019;2(1):40-9.

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