The global dynamics of a new fractional-order chaotic system

被引：6
作者：
Liu, Ping [1 ]
Zhang, Yulan [2 ]
Mohammed, Khidhair Jasim [3 ]
Lopes, Antonio M. [4 ]
Saberi-Nik, Hassan [5 ]
机构：
[1] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China
[2] Southwest Univ, High Sch, Chongqing 400715, Peoples R China
[3] Al Mustaqbal Univ Coll, Air Conditioning & Refrigerat Tech Engn Dept, Babylon 51001, Iraq
[4] Univ Porto, Fac Engn, LAETA, INEGI, Rua Dr Roberto Frias, P-4200465 Porto, Portugal
[5] Univ Neyshabur, Dept Math & Stat, Neyshabur, Iran
来源：
CHAOS SOLITONS & FRACTALS | 2023年 / 175卷
关键词：
Fractional-order chaotic system; Global Mittag-Leffler attractive set; Chaos control; Hamilton energy; ULTIMATE BOUND SETS; LORENZ; SYNCHRONIZATION; IMPLEMENTATION; ATTRACTORS;
D O I：
10.1016/j.chaos.2023.114006
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper investigates the global dynamics of a new 3-dimensional fractional-order (FO) system that presents just cross-product nonlinearities. Firstly, the FO forced Lorenz-84 system is introduced and the stability of its equilibrium points, as well as the chaos control for their stabilization, are addressed. Secondly, dynamical behavior is further analyzed and bifurcation diagrams, phase portraits, and largest Lyapunov exponent (LE) are discussed. Then, the global Mittag-Leffler attractive sets (MLASs) and Mittag-Leffler positive invariant sets (MLPISs) of the FO forced Lorenz-84 system are presented. Finally, the Hamilton energy function (HEF) of the Lorenz-84 system is calculated by using the Helmholtz theorem. The calculation of the Hamilton energy has an essential role on the estimation of chaos in dynamical systems, the guidance of orbits, and stability. In fact, any control action on the dynamical system completely changes the HEF. Numerical simulations are presented for illustrating the theoretical findings.
引用
收藏
页数：12
相关论文
共 46 条
  • [1] On some Routh-Hurwitz conditions for fractional order differential equations and their applications in Lorenz, Rossler, Chua and Chen systems
    Ahmed, E.
    El-Sayed, A. M. A.
    El-Saka, Hala A. A.
    [J]. PHYSICS LETTERS A, 2006, 358 (01) : 1 - 4
  • [2] [Anonymous], 2020, NONLINEAR DYNAM, DOI DOI 10.1007/s11071-020-05637-z
  • [3] A fractional order optimal 4D chaotic financial model with Mittag-Leffler law
    Atangana, A.
    Bonyah, E.
    Elsadany, A. A.
    [J]. CHINESE JOURNAL OF PHYSICS, 2020, 65 : 38 - 53
  • [4] Complex-order fractional diffusion in reaction-diffusion systems
    Bueno-Orovio, Alfonso
    Burrage, Kevin
    [J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2023, 119
  • [5] Stabilization and destabilization of fractional oscillators via a delayed feedback control
    Cermak, Jan
    Kisela, Tomas
    [J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2023, 117
  • [6] Predicting the chaos and solution bounds in a complex dynamical system
    Chien, Fengsheng
    Inc, Mustafa
    Yosefzade, Hamidreza
    Nik, Hassan Saberi
    [J]. CHAOS SOLITONS & FRACTALS, 2021, 153
  • [7] Competitive modes and estimation of ultimate bound sets for a chaotic dynamical financial system
    Chien, Fengsheng
    Chowdhury, A. Roy
    Nik, Hassan Saberi
    [J]. NONLINEAR DYNAMICS, 2021, 106 (04) : 3601 - 3614
  • [8] Symmetry-breaking and bifurcation diagrams of fractional-order maps
    Danca, Marius -F.
    [J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2023, 116
  • [9] Multistability, phase diagrams, and intransitivity in the Lorenz-84 low-order atmospheric circulation model
    Freire, Joana G.
    Bonatto, Cristian
    DaCamara, Carlos C.
    Gallas, Jason A. C.
    [J]. CHAOS, 2008, 18 (03)
  • [10] Boundedness and convergence on fractional order systems
    Gallegos, Javier A.
    Duarte-Mermoud, Manuel A.
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2016, 296 : 815 - 826
12345