On the Global Asymptotic Stability and 4-Period Oscillation of the Third-Order Difference Equation

IF 1.2 Q2 MATHEMATICS, APPLIED

Journal of Applied Mathematics Pub Date : 2023-11-11 DOI:10.1155/2023/5726617

M. E. Erdogan

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引用次数: 0

Abstract

The main objective of this paper is to study the global behavior and oscillation of the following third-order rational difference equation

x_{n + 1} = α x_{n} x_{n - 1} x_{n - 2} / β x_{n - 1}^{2} + γ x_{n - 2}^{2}

, where the initial conditions

x_{- 2}, x_{- 1}, x_{0}

are nonzero real numbers and

α, β, γ

are positive constants such that

α \leq β + γ

. Visual examples supporting solutions are given at the end of the study. The figures are found with the help of MATLAB.

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三阶差分方程的全局渐近稳定性和4周期振荡

本文的主要目的是研究全球行为和振荡的三阶有理差分方程x n + 1 =αx n n−1 x n−2 /βx n−1 2 +γx n−2 2,初始条件x−2,x−1,x非零实数和α,β,γ是积极的常量,α≤β+γ。在研究的最后给出了支持解决方案的可视化示例。图形是借助MATLAB软件进行绘制的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Applied Mathematics MATHEMATICS, APPLIED-

CiteScore

2.70

自引率

0.00%

发文量

审稿时长

3.2 months

期刊介绍： Journal of Applied Mathematics is a refereed journal devoted to the publication of original research papers and review articles in all areas of applied, computational, and industrial mathematics.