Global behavior of positive solutions of a third order difference equations system

Document Type : Research Paper

Author

Department of Mathematical Analysis, University of Transport and Communications, Hanoi, Vietnam

Abstract

In this paper, we investigate the global behavior of positive solutions of the system of difference equations
\begin{equation*}
x_{n+1}=\alpha+ \dfrac{y^p_{n}}{y^p_{n-2}},\
y_{n+1}=\alpha+ \dfrac{x^q_{n} }{x^q_{n-2}},
\ n=0, 1, 2, ...
\end{equation*}
where parameters $\alpha, p, q \in (0, \infty)$ and the initial values $x_{i}$, $y_{i}$ are arbitrary positive numbers for $ i= -2,-1, 0$. Moreover, the rate of convergence of positive solutions is established and some numerical examples are given to demonstrate our theoretical results.

Keywords

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Volume 14, Issue 1
January 2023
Pages 3189-3200
  • Receive Date: 15 October 2022
  • Revise Date: 04 January 2023
  • Accept Date: 12 January 2023