Neimark-Sacker Bifurcation of a Third Order Difference Equation

Year 2019, , 40 - 49, 17.06.2019

Marwan Aloqeili , Asmaa Shareef

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

Cited By: 1

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.