Global dynamics of two systems of exponential difference equations by Lyapunov function

In this paper, we study the boundedness character and persistence, existence and uniqueness of the positive equilibrium, local and global behavior, and rate of convergence of positive solutions of two systems of exponential difference equations.Furthermore, by constructing a discrete Lyapunov function, we obtain the global asymptotic stability of the unique positive equilibrium point.Some numerical examples are given to verify our theoretical results.