Global dynamics of some system of second-order difference equations

  • Received: 01 June 2021 Published: 08 October 2021
  • Primary: 39A10, 39A30; Secondary: 40A05

  • In this paper, we study the boundedness and persistence of positive solution, existence of invariant rectangle, local and global behavior, and rate of convergence of positive solutions of the following systems of exponential difference equations

    $ \begin{align*} x_{n+1} = \dfrac{\alpha_1+\beta_1e^{-x_{n-1}}}{\gamma_1+y_n},\ y_{n+1} = \dfrac{\alpha_2+\beta_2e^{-y_{n-1}}}{\gamma_2+x_n},\\ x_{n+1} = \dfrac{\alpha_1+\beta_1e^{-y_{n-1}}}{\gamma_1+x_n},\ y_{n+1} = \dfrac{\alpha_2+\beta_2e^{-x_{n-1}}}{\gamma_2+y_n}, \end{align*} $

    where the parameters $ \alpha_i,\ \beta_i,\ \gamma_i $ for $ i \in \{1,2\} $ and the initial conditions $ x_{-1}, x_0, y_{-1}, y_0 $ are positive real numbers. Some numerical example are given to illustrate our theoretical results.

    Citation: Tran Hong Thai, Nguyen Anh Dai, Pham Tuan Anh. Global dynamics of some system of second-order difference equations[J]. Electronic Research Archive, 2021, 29(6): 4159-4175. doi: 10.3934/era.2021077

    Related Papers:

  • In this paper, we study the boundedness and persistence of positive solution, existence of invariant rectangle, local and global behavior, and rate of convergence of positive solutions of the following systems of exponential difference equations

    $ \begin{align*} x_{n+1} = \dfrac{\alpha_1+\beta_1e^{-x_{n-1}}}{\gamma_1+y_n},\ y_{n+1} = \dfrac{\alpha_2+\beta_2e^{-y_{n-1}}}{\gamma_2+x_n},\\ x_{n+1} = \dfrac{\alpha_1+\beta_1e^{-y_{n-1}}}{\gamma_1+x_n},\ y_{n+1} = \dfrac{\alpha_2+\beta_2e^{-x_{n-1}}}{\gamma_2+y_n}, \end{align*} $

    where the parameters $ \alpha_i,\ \beta_i,\ \gamma_i $ for $ i \in \{1,2\} $ and the initial conditions $ x_{-1}, x_0, y_{-1}, y_0 $ are positive real numbers. Some numerical example are given to illustrate our theoretical results.



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