Dynamical Behavior of Solutions to Higher-Order System of Fuzzy Difference Equations

Abstract

In this paper, we concentrate on the global behavior of the fuzzy difference equations system with higher order \begin{eqnarray}\nonumber \alpha_{n+1}=\tau_1+\frac{\alpha_n}{\sum_{i=1}^{m}\beta_{n-i}}, \beta_{n+1}=\tau_2+\frac{\beta_n}{\sum_{i=1}^{m}\alpha_{n-i}}, \quad n\in \mathbb{N}_0, \end{eqnarray} where $\alpha_n, \beta_n$ are positive fuzzy number sequences, parameters $\tau_1, \tau_2$ and the initial values $\alpha_{-i}, \beta_{-i}, i \in \{0, 1, \dots, m\}$, are positive fuzzy numbers. Firstly, we show the existence and uniqueness of the positive fuzzy solution to the mentioned system. Furthermore, we are searching for the boundedness, persistence and convergence of the positive solution to the given system. Finally, we give some numerical examples to show the efficiency of our results.

Keywords

• Fuzzy difference equations system
• Positive fuzzy solution
• Dynamical behavior

References

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