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.
Primary Language | English |
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Subjects | Mathematical Sciences |
Journal Section | Articles |
Authors | |
Publication Date | June 30, 2022 |
Submission Date | November 24, 2021 |
Acceptance Date | April 21, 2022 |
Published in Issue | Year 2022 Volume: 5 Issue: 2 |
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