Global behavior of positive solutions of a third order difference equations system
Abstract
\begin{abstract} In this paper, we consider the following system of difference equations \begin{equation*} x_{n+1}=\alpha+\dfrac{y_{n}^p}{y_{n2}^p},\ y_{n+1}=\alpha+ \dfrac{x_{n}^q}{x_{n2}^q}, \ 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$. Our main aim is to investigate semicycle analysis of solutions of above system. Also, we study the boundedness of the positive solutions and the global asymptotic stability of the equilibrium point in case $\alpha>1$, $ 0<p,\ q\leq 1$. Moreover, the rate of convergence of the solutions is established. Finally, some numerical examples are given to illustrate our theoretical results.
 Publication:

arXiv eprints
 Pub Date:
 August 2021
 DOI:
 10.48550/arXiv.2108.05534
 arXiv:
 arXiv:2108.05534
 Bibcode:
 2021arXiv210805534P
 Keywords:

 Mathematics  Classical Analysis and ODEs;
 39A10