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Global behavior of positive solutions of a third order difference equations system
  • Phong Mai
Phong Mai
University of Transport and Communication

Corresponding Author:[email protected]

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In this paper, by using semi-cycle analysis method we examine the behavior of positive solutions of the system of difference equations \begin{equation*} x_{n+1}=\alpha+\dfrac{y_{n}^p}{y_{n-2}^p},\ y_{n+1}=\alpha+ \dfrac{x_{n}^q}{x_{n-2}^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$. We also study the boundedness of positive solutions, the global asymptotic stability of the equilibrium point of above system in the case of $\alpha>1$, $0