Abstract Fractional calculus is a 300 years topic, which has been introduced to real physics systems modeling and engineering applications. In the last few decades, fractional-order nonlinear chaotic systems have been widely investigated. Firstly, the most used methods to solve fractional-order chaotic systems are reviewed. Characteristics and memory effect in those method are summarized. Then we discuss the memory effect in the fractional-order chaotic systems through the fractional-order calculus and numerical solution algorithms. It shows that the integer-order derivative has full memory effect, while the fractional-order derivative has nonideal memory effect due to the kernel function. Memory loss and short memory are discussed. Finally, applications of the fractional-order chaotic systems regarding the memory effects are investigated. The work summarized in this manuscript provides reference value for the applied scientists and engineering community of fractional-order nonlinear chaotic systems.
Fund: Project supported by the Natural Science Foundation of China (Grant Nos. 61901530, 62071496, and 62061008) and the Natural Science Foundation of Hunan Province, China (Grant No. 2020JJ5767).
Corresponding Authors:
Huihai Wang
E-mail: wanghuihai_csu@csu.edu.cn
Cite this article:
Shaobo He(贺少波), Huihai Wang(王会海), and Kehui Sun(孙克辉) Solutions and memory effect of fractional-order chaotic system: A review 2022 Chin. Phys. B 31 060501
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