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

被引：3
|
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.
引用
收藏
页数：16
相关论文
共 50 条
  • [1] Dynamical analysis, control, boundedness, and prediction for a fractional-order financial risk system
    杨轲皓
    郑松
    余天虎
    Aceng Sambas
    Muhamad Deni Johansyah
    Hassan SaberiNik
    Mohamad Afendee Mohamed
    Chinese Physics B, 2024, 33 (11) : 263 - 275
  • [2] Dynamical analysis, control, boundedness, and prediction for a fractional-order financial risk system
    Yang, Kehao
    Zheng, Song
    Yu, Tianhu
    Sambas, Aceng
    Johansyah, Muhamad Deni
    Saberi-Nik, Hassan
    Mohamed, Mohamad Afendee
    Chinese Physics B, 2024, 33 (11)
  • [3] Dynamical behaviour of fractional-order finance system
    Farman, Muhammad
    Akguel, Ali
    Saleem, Muhammad Umer
    Imtiaz, Sumaiyah
    Ahmad, Aqeel
    PRAMANA-JOURNAL OF PHYSICS, 2020, 94 (01):
  • [4] Dynamical behaviour of fractional-order finance system
    Muhammad Farman
    Ali Akgül
    Muhammad Umer Saleem
    Sumaiyah Imtiaz
    Aqeel Ahmad
    Pramana, 2020, 94
  • [5] Dynamical analysis and adaptive fuzzy control for the fractional-order financial risk chaotic system
    Aceng Sukono
    Shaobo Sambas
    Heng He
    Sundarapandian Liu
    Yuyun Vaidyanathan
    Jumadil Hidayat
    Advances in Difference Equations, 2020
  • [6] Dynamical analysis and adaptive fuzzy control for the fractional-order financial risk chaotic system
    Sukono
    Sambas, Aceng
    He, Shaobo
    Liu, Heng
    Vaidyanathan, Sundarapandian
    Hidayat, Yuyun
    Saputra, Jumadil
    ADVANCES IN DIFFERENCE EQUATIONS, 2020, 2020 (01)
  • [7] Control fractional-order continuous chaotic system via a simple fractional-order controller
    Zhang, Dong
    Yang, Shou-liang
    INDUSTRIAL INSTRUMENTATION AND CONTROL SYSTEMS II, PTS 1-3, 2013, 336-338 : 770 - 773
  • [8] Control and Synchronization of the Fractional-Order Lorenz Chaotic System via Fractional-Order Derivative
    Zhou, Ping
    Ding, Rui
    MATHEMATICAL PROBLEMS IN ENGINEERING, 2012, 2012
  • [9] Adaptive control and synchronization of a fractional-order chaotic system
    Li, Chunlai
    Tong, Yaonan
    PRAMANA-JOURNAL OF PHYSICS, 2013, 80 (04): : 583 - 592
  • [10] Projective synchronization control of fractional-order chaotic system
    Zhang, Fandi
    PROCEEDINGS OF THE 2018 8TH INTERNATIONAL CONFERENCE ON APPLIED SCIENCE, ENGINEERING AND TECHNOLOGY (ICASET 2018), 2018, 159 : 161 - 164
12345