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In this paper, we explore the boundedness and persistence of positive solution, existence as well as uniqueness of positive equilibrium point, existence of invariant rectangle, local and global dynamics, and rate of convergence of three-directional discrete-time exponential system. Finally, numerical simulations are given to verify not only obtained results but also to have the appearance of stable invariant close curves. The appearance of close curves grantee the fact that the system undergoes a supercritical hopf bifurcation.