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Aiming at the complexity problem of fractional-order Jafari-Sprott chaotic system, in this paper, Adomian decomposition method is used to study its numerical analysis and a complexity analysis method of fractional-order Jafari-Sprott chaotic system based on fuzzy entropy algorithm, sample entropy algorithm and dispersion entropy algorithm is proposed. For the synchronization and control of fractional-order Jafari-Sprott chaotic system, sliding mode control is used to achieve synchronization of fractional-order Jafari-Sprott chaotic system and a control method of fractional-order Jafari-Sprott chaotic system is proposed based on frequency distribution model of fractional-order integral operator. The main results are as follows: (1) The complexity of the fractional-order Jafari-Sprott chaotic system is greater than the integer-order Jafari-Sprott chaotic system, and fractional-order chaotic system has better application prospects. (2) Moreover, it is concluded that the effect of the dispersion entropy algorithm on detecting complexity is the best, which provides theoretical and experimental basis for the practical engineering application of the fractional-order Jafari-Sprott chaotic system. (3) Synchronization and control of fractional-order Jafari-Sprott chaotic system is accomplished by sliding model control and frequency distribution model of fractional-order integral operator respectively. In particular, the control effect of each variable is accomplished by designing a control law based on the frequency distribution model of fractional integral operator.

Complexity Analysis and Synchronization Control of Fractional-Order Jafari-Sprott Chaotic System