Abstract
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_{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.
Highlights
In the past five decades, fractional-order chaotic systems have received increasing attention since fractional derivatives provide a memory effect
5 Conclusions In this paper, I investigated the chaotic dynamics of the discrete reduced Lorenz map obtained by means of the discrete fractional calculus
Lorenz map of fractional difference order is given in the form of an iteration formula
Summary
In the past five decades, fractional-order chaotic systems have received increasing attention since fractional derivatives provide a memory effect. Many important and interesting research work on the chaotic dynamics of fractional-order chaotic systems can be found in [1,2,3]. A lot of important research about the dynamics of discrete fractional equations can be found in [12,13,14,15,16,17,18,19,20,21,22,23,24] and the references therein. Many results have been presented, the chaotic dynamics, especially, the identification of chaos and bifurcation behaviors, in the discrete fractional chaotic systems are still kept open and deserve further investigation. The complexity measure of chaotic sequences in the discrete fractional difference systems have been rarely reported.
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