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

doi:10.1088/1674-1056/ac43ae

中国物理B ›› 2022, Vol. 31 ›› Issue (6): 60501-060501.doi: 10.1088/1674-1056/ac43ae

所属专题： SPECIAL TOPIC — Interdisciplinary physics: Complex network dynamics and emerging technologies

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

收稿日期:2021-09-22 修回日期:2021-12-09 接受日期:2021-12-16 出版日期:2022-05-17 发布日期:2022-05-19
通讯作者: Huihai Wang E-mail:wanghuihai_csu@csu.edu.cn
基金资助:
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).

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

Received:2021-09-22 Revised:2021-12-09 Accepted:2021-12-16 Online:2022-05-17 Published:2022-05-19
Contact: Huihai Wang E-mail:wanghuihai_csu@csu.edu.cn
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: fractional calculus, fractional-order chaotic system, numerical approximation, memory effect

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.

Key words: fractional calculus, fractional-order chaotic system, numerical approximation, memory effect

中图分类号: (Numerical simulations of chaotic systems)

05.45.Pq

05.45.-a (Nonlinear dynamics and chaos)

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[J]. 中国物理B, 2022, 31(6): 60501-060501.

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[J]. Chin. Phys. B, 2022, 31(6): 60501-060501.

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