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

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 syste...

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Veröffentlicht in:Chinese physics B 2022-05, Vol.31 (6), p.60501-30
Hauptverfasser: He, Shaobo, Wang, Huihai, Sun, Kehui
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:1674-1056
DOI:10.1088/1674-1056/ac43ae