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

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Communications in Advanced Mathematical Sciences
Volume:5 Issue:2
Dynamics and Bifurcation of $x_{n+1}=frac{alpha+beta x_{n-1}}{A+Bx_{n}+C x_{n-1}}$

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

Authors : Mohammad SALEH, Batool RADDAD

Pages : 78-87

Doi:10.33434/cams.1028122

View : 44 | Download : 9

Publication Date : 2022-06-30

Article Type : Research Paper

Abstract :The main goal of this paper is to study the bifurcation of a second order rational difference equation $$x_{n+1}=\frac{\alpha+\beta x_{n-1}}{A+Bx_{n}+Cx_{n-1}}, ~~n=0, 1, 2, \ldots$$ 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 and the direction of the bifurcation of the period-two cycle. Numerical discussion with figures are given to support our results.
Keywords : stability, bifurcation, chaos

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