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

被引:23
|
作者
He, Shaobo [1 ]
Wang, Huihai [1 ]
Sun, Kehui [1 ]
机构
[1] Cent South Univ, Sch Phys & Elect, Changsha 410083, Peoples R China
关键词
fractional calculus; fractional-order chaotic system; numerical approximation; memory effect; PREDICTOR-CORRECTOR APPROACH; DIFFERENTIAL-EQUATIONS; CIRCUIT IMPLEMENTATION; FPGA IMPLEMENTATION; ADAPTIVE SYNCHRONIZATION; NONLINEAR DYNAMICS; NEURAL-NETWORK; ERROR ANALYSIS; CHEN SYSTEM; MODEL;
D O I
10.1088/1674-1056/ac43ae
中图分类号
O4 [物理学];
学科分类号
0702 ;
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.
引用
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页数:21
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