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Dynamical Behavior of a Third-Order Difference Equation with Arbitrary Powers

Ozkan Ocalan|Mehmet Gumus|Raafat Abo-Zeid
경북대학교 자연과학대학 수학과|2017.06|Kyungpook Mathematical Journal|제57권 제2호|pp. 251-263

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키워드

boundednessperiodicityglobal stabilityequilibrium pointsolution.
주제분류수학

초록

The aim of this paper is to investigate the dynamical behavior of thedifference equation%\begin{equation*}x_{n+1}=\frac{\alpha x_{n}}{\beta +\gamma x_{n-1}^{p}x_{n-2}^{q}},\text{ }n=0,1,\ldots,\end{equation*}where the parameters $\alpha ,\beta ,\gamma ,p,q$ are non-negative numbersand the initial values $x_{-2}$,$x_{-1},x_{0}$ are positive numbers. Also,some numerical examples are given to verify our theoretical results.

Abstract

The aim of this paper is to investigate the dynamical behavior of thedifference equation%\begin{equation*}x_{n+1}=\frac{\alpha x_{n}}{\beta +\gamma x_{n-1}^{p}x_{n-2}^{q}},\text{ }n=0,1,\ldots,\end{equation*}where the parameters $\alpha ,\beta ,\gamma ,p,q$ are non-negative numbersand the initial values $x_{-2}$,$x_{-1},x_{0}$ are positive numbers. Also,some numerical examples are given to verify our theoretical results.

참고문헌 (23)

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