In this paper, a two-dimensional discrete fractional reduced Lorenz map is achieved by utilizing discrete fractional calculus. By adopting the bifurcation diagrams, chaos diagram, and phase portraits, the chaotic dynamics of the two-dimensional discrete fractional reduced Lorenz map are analyzed. Complexity of this fractional map versus parameters is discussed by employing the C 0 algorithm. It is found that this fractional map has rich dynamical behaviors. In addition, it also shows that the C

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... 0 algorithm provides a parameter choice method for practice applications of discrete fractional maps. Finally, some numerical simulations are given to demonstrate the effectiveness of the proposed results.