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Dynamics of the Rational Difference Equation $x_{n+1}=px_{n}+\frac{q}{x_{n-1}^2}$
This version is not peer-reviewed.
Submitted:
06 April 2020
Posted:
08 April 2020
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Abstract
A second order rational difference equation $$x_{n+1}=px_{n}+\frac{q}{x_{n-1}^2}$$ with the parameters $p$ and $q$ which lies in $(0,1)$, is studied. The dynamics of the equilibrium is characterized through the trichotomy of the parameter $p<\frac{1}{2}$, $p=\frac{1}{2}$ and $p>\frac{1}{2}$. It is found that there is no periodic solution of period $2$ and $3$ but there exists periodic solutions with only periodic solution $5$ and $10$ are achieved computationally.
Keywords:
rational difference equation
; asymptotic stability
; periodic solutions
; chaos and fractal
Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.
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