Dynamical Behaviour, Control, and Boundedness of a Fractional-Order Chaotic System

被引：7
作者：
Ren, Lei [1 ]
Muhsen, Sami [2 ]
Shateyi, Stanford [3 ]
Saberi-Nik, Hassan [4 ]
机构：
[1] Shangqiu Normal Univ, Sch Math & Stat, Shangqiu 476000, Peoples R China
[2] Al Mustaqbal Univ, Coll Engn & Technol, Air Conditioning & Refrigerat Tech Engn Dept, Babylon 51001, Iraq
[3] Univ Venda, Dept Math, Private Bag X5050, ZA-0950 Thohoyandou, South Africa
[4] Univ Neyshabur, Dept Math & Stat, Neyshabur 9319774446, Iran
来源：
FRACTAL AND FRACTIONAL | 2023年 / 7卷 / 07期
关键词：
fractional-order hyperchaotic system; global Mittag-Leffler attractive sets (MLASs); Mittag-Leffler positive invariant sets (MLPISs); chaos control; ULTIMATE BOUND SETS; LORENZ; SYNCHRONIZATION;
D O I：
10.3390/fractalfract7070492
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, the fractional-order chaotic system form of a four-dimensional system with cross-product nonlinearities is introduced. The stability of the equilibrium points of the system and then the feedback control design to achieve this goal have been analyzed. Furthermore, further dynamical behaviors including, phase portraits, bifurcation diagrams, and the largest Lyapunov exponent are presented. Finally, the global Mittag-Leffler attractive sets (MLASs) and Mittag-Leffler positive invariant sets (MLPISs) of the considered fractional order system are presented. Numerical simulations are provided to show the effectiveness of the results.
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页数：16
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