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Chin. Phys. B, 2022, Vol. 31(6): 060501    DOI: 10.1088/1674-1056/ac43ae
Special Issue: SPECIAL TOPIC— Interdisciplinary physics: Complex network dynamics and emerging technologies
TOPICAL REVIEW—Interdisciplinary physics: Complex network dynamics and emerging technologies Prev   Next  

Solutions and memory effect of fractional-order chaotic system: A review

Shaobo He(贺少波), Huihai Wang(王会海), and Kehui Sun(孙克辉)
School of Physics and Electronics, Central South University, Changsha 410083, China
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.
Keywords:  fractional calculus      fractional-order chaotic system      numerical approximation      memory effect  
Received:  22 September 2021      Revised:  09 December 2021      Accepted manuscript online:  16 December 2021
PACS:  05.45.Pq (Numerical simulations of chaotic systems)  
  05.45.-a (Nonlinear dynamics and chaos)  
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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