The global dynamics of a new fractional-order chaotic system

被引：8
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.
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页数：12
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