Global dynamics of some \(3 \times 6\) systems of exponential difference equations (Q1727276)

Summary: We study the global dynamics of a list of following \(3 \times 6\) systems of exponential difference equations: \(x_{n+1}=(\alpha_4+\beta_4e^{-y_n})/(\gamma_4+y_{n-1})\), \(y_{n+1}=(\alpha_5+\beta_5e^{-z_n})/(\gamma_5+z_{n-1})\), \(z_{n+1}=(\alpha_6+\beta_6e^{-x_n})/(\gamma_6+x_{n-1})\), \(x_{n+1}=(\alpha_7+\beta_7e^{-z_n})/(\gamma_7+z_{n-1})\), \(y_{n+1}=(\alpha_8+\beta_8e^{-x_n})/(\gamma_8+x_{n-1})\), \(z_{n+1}=(\alpha_9+\beta_9e^{-y_n})/(\gamma_9+y_{n-1})\), \(x_{n+1}=(\alpha_{10}+\beta_{10}e^{-x_n})/(\gamma_{10}+x_{n-1})\), \(y_{n+1}=(\alpha_{11}+\beta_{11}e^{-y_n})/(\gamma_{11}+z_{n-1})\), \(z_{n+1}=(\alpha_{12}+\beta_{12}e^{-z_n})/(\gamma_{12}+y_{n-1})\), \(x_{n+1}=(\alpha_{13}+\beta_{13}e^{-x_n})/(\gamma_{13}+z_{n-1})\), \(y_{n+1}=(\alpha_{14}+\beta_{14}e^{-y_n})/(\gamma_{14}+y_{n-1})\), \(z_{n+1}=(\alpha_{15}+\beta_{15}e^{-z_n})/(\gamma_{15}+x_{n-1})\), \(x_{n+1}=(\alpha_{16}+\beta_{16}e^{-x_n})/(\gamma_{16}+y_{n-1})\), \(y_{n+1}=(\alpha_{17}+\beta_{17}e^{-y_n})/(\gamma_{17}+x_{n-1})\), \(z_{n+1}=(\alpha_{18}+\beta_{13}e^{-z_n})/(\gamma_{18}+z_{n-1})\), where \(\alpha_i\), \(\beta_i\), \(\gamma_i\), \(i=4,5,\dots,18\) and the initial conditions \(x_0\), \(x_{-1}\), \(y_0\), \(y_{-1}\), \(z_0\), \(z_{-1}\) are arbitrary nonnegative real numbers. This proposed work is considerably extended and improve some existing results in the literature. Some numerical examples are given to not only verify our theoretical results but also provide different types of qualitative behavior of solution of these systems.