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. INDEX TERMS Fractional-order chaotic system, Adomian decomposition method, complexity analysis, sliding mode control, frequency distribution model of fractional-order integral operator. I. INTRODUCTION Research on complexity is involved in various fields. So far there is no unified concept of complexity. Complexity refers to metric value, which has comparative significance, and different complexity algorithms characterize different aspects of complexity. Horgan [1] pointed out that there are multiple definitions of complexity, such as time complexity, space complexity, semantic complexity, Kolmogorov complexity, etc. There are multiple algorithms for calculating complexity. Lempel and Ziv [2] proposed Lempl-Ziv algorithm. Pincus [3] and Sun et al. [4] proposed an approximate entropy algorithm. Chen et al. [5] and Sun et al. [6] proposed a fuzzy entropy algorithm. Larrondo et al. [7] and Sun et al. [8] proposed a strength statistics algorithm. Azad et al. [9] proposed a symbolic entropy algorithm. At present, there are spectral entropy algorithm [10], wavelet entropy algo-The associate editor coordinating the review of this manuscript and approving it for publication was Di He .
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