Neimark-Sacker Bifurcation of a Third Order Difference Equation

Marwan Aloqeili; Asmaa Shareef

doi:10.33401/fujma.527572

Research Article

Neimark-Sacker Bifurcation of a Third Order Difference Equation

Year 2019, Volume: 2 Issue: 1, 40 - 49, 17.06.2019

Marwan Aloqeili , Asmaa Shareef

https://doi.org/10.33401/fujma.527572

Cited By: 2

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.

Keywords

Difference equation , Stability , Equilibrium , Neimark-Sacker Bifurcation , Stability

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

Marwan Aloqeili , Asmaa Shareef

https://doi.org/10.33401/fujma.527572

Cited By: 2

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 (June2019), 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.