Yıl: 2021 Cilt: 4 Sayı: 1 Sayfa Aralığı: 25 - 37 Metin Dili: İngilizce DOI: 10.33187/jmsm.843626 İndeks Tarihi: 29-07-2022

Dynamics and Bifurcation of$x_{n+1}=frac{alpha+beta x_{n-2}}{A+Bx_{n}+C x_{n-2}}$

Öz:
In this paper, we study dynamics and bifurcation of the third order rational difference equation begin{eqnarray*} x_{n+1}=frac{alpha+beta x_{n-2}}{A+Bx_{n}+Cx_{n-2}}, ~~n=0, 1, 2, ldots end{eqnarray*} with positive parameters $alpha, beta, A, B, C$ and non-negative initial conditions ${x_{-k}, x_{-k+1}, ldots, x_{0}}$. We study the dynamic behavior, the sufficient conditions for the existence of the Neimark-Sacker bifurcation, and the direction of the Neimark-Sacker bifurcation. Then, we give numerical examples with figures to support our results.
Anahtar Kelime: Stability Bifurcation Fixed points

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
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APA Raddad B, Saleh M (2021). Dynamics and Bifurcation of$x_{n+1}=frac{alpha+beta x_{n-2}}{A+Bx_{n}+C x_{n-2}}$. , 25 - 37. 10.33187/jmsm.843626
Chicago Raddad Batool,Saleh Mohammad Dynamics and Bifurcation of$x_{n+1}=frac{alpha+beta x_{n-2}}{A+Bx_{n}+C x_{n-2}}$. (2021): 25 - 37. 10.33187/jmsm.843626
MLA Raddad Batool,Saleh Mohammad Dynamics and Bifurcation of$x_{n+1}=frac{alpha+beta x_{n-2}}{A+Bx_{n}+C x_{n-2}}$. , 2021, ss.25 - 37. 10.33187/jmsm.843626
AMA Raddad B,Saleh M Dynamics and Bifurcation of$x_{n+1}=frac{alpha+beta x_{n-2}}{A+Bx_{n}+C x_{n-2}}$. . 2021; 25 - 37. 10.33187/jmsm.843626
Vancouver Raddad B,Saleh M Dynamics and Bifurcation of$x_{n+1}=frac{alpha+beta x_{n-2}}{A+Bx_{n}+C x_{n-2}}$. . 2021; 25 - 37. 10.33187/jmsm.843626
IEEE Raddad B,Saleh M "Dynamics and Bifurcation of$x_{n+1}=frac{alpha+beta x_{n-2}}{A+Bx_{n}+C x_{n-2}}$." , ss.25 - 37, 2021. 10.33187/jmsm.843626
ISNAD Raddad, Batool - Saleh, Mohammad. "Dynamics and Bifurcation of$x_{n+1}=frac{alpha+beta x_{n-2}}{A+Bx_{n}+C x_{n-2}}$". (2021), 25-37. https://doi.org/10.33187/jmsm.843626
APA Raddad B, Saleh M (2021). Dynamics and Bifurcation of$x_{n+1}=frac{alpha+beta x_{n-2}}{A+Bx_{n}+C x_{n-2}}$. Journal of mathematical sciences and modelling (Online), 4(1), 25 - 37. 10.33187/jmsm.843626
Chicago Raddad Batool,Saleh Mohammad Dynamics and Bifurcation of$x_{n+1}=frac{alpha+beta x_{n-2}}{A+Bx_{n}+C x_{n-2}}$. Journal of mathematical sciences and modelling (Online) 4, no.1 (2021): 25 - 37. 10.33187/jmsm.843626
MLA Raddad Batool,Saleh Mohammad Dynamics and Bifurcation of$x_{n+1}=frac{alpha+beta x_{n-2}}{A+Bx_{n}+C x_{n-2}}$. Journal of mathematical sciences and modelling (Online), vol.4, no.1, 2021, ss.25 - 37. 10.33187/jmsm.843626
AMA Raddad B,Saleh M Dynamics and Bifurcation of$x_{n+1}=frac{alpha+beta x_{n-2}}{A+Bx_{n}+C x_{n-2}}$. Journal of mathematical sciences and modelling (Online). 2021; 4(1): 25 - 37. 10.33187/jmsm.843626
Vancouver Raddad B,Saleh M Dynamics and Bifurcation of$x_{n+1}=frac{alpha+beta x_{n-2}}{A+Bx_{n}+C x_{n-2}}$. Journal of mathematical sciences and modelling (Online). 2021; 4(1): 25 - 37. 10.33187/jmsm.843626
IEEE Raddad B,Saleh M "Dynamics and Bifurcation of$x_{n+1}=frac{alpha+beta x_{n-2}}{A+Bx_{n}+C x_{n-2}}$." Journal of mathematical sciences and modelling (Online), 4, ss.25 - 37, 2021. 10.33187/jmsm.843626
ISNAD Raddad, Batool - Saleh, Mohammad. "Dynamics and Bifurcation of$x_{n+1}=frac{alpha+beta x_{n-2}}{A+Bx_{n}+C x_{n-2}}$". Journal of mathematical sciences and modelling (Online) 4/1 (2021), 25-37. https://doi.org/10.33187/jmsm.843626