On the Three-Dimensional Fractional-Order Henon Map with Lorenz-Like Attractors

被引：15

作者：

Khennaoui, Amina-Aicha ^{[1
]}

Ouannas, Adel ^{[2
]}

Odibat, Zaid ^{[3
]}

Viet-Thanh Pham ^{[4
,5
]}

Grassi, Giuseppe ^{[6
]}

机构：

[1] Univ Larbi Ben Mhidi, Lab Dynam Syst & Control, Oum El Bouaghi, Algeria

[2] Univ Larbi Tebessi, Lab Math Informat & Syst LAMIS, Tebessa 12002, Algeria

[3] Al Balqa Appl Univ, Dept Math, Fac Sci, Salt 19117, Jordan

[4] Phenikaa Univ, Phenikaa Inst Adv Study PIAS, Fac Elect & Elect Engn, Hanoi 100000, Vietnam

[5] A&A Green Phoenix Grp, Phenikaa Res & Technol Inst PRATI, 167 Hoang Ngan, Hanoi 100000, Vietnam

[6] Univ Salento, Dipartimento Ingn Innovaz, I-73100 Lecce, Italy

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2020年 / 30卷 / 11期

关键词：

Fractional discrete-time calculus; Caputo-like difference operator; chaos; Henon-like map; control; synchronization; CHAOS SYNCHRONIZATION; STABILITY; COEXISTENCE; SYSTEMS; DIFFEOMORPHISMS; BIFURCATIONS; CALCULUS; SCHEME;

D O I：

10.1142/S021812742050217X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A three-dimensional (3D) Henon map of fractional order is proposed in this paper. The dynamics of the suggested map are numerically illustrated for different fractional orders using phase plots and bifurcation diagrams. Lorenz-like attractors for the considered map are realized. Then, using the linear fractional-order systems stability criterion, a controller is proposed to globally stabilize the fractional-order Henon map. Furthermore, synchronization control scheme has been designed to exhibit a synchronization behavior between a given 2D fractional-order chaotic map and the 3D fractional-order Henon map. Numerical simulations are also performed to verify the main results of the study.

引用

页数：16

共 50 条

[1] Three-dimensional Henon-like maps and wild Lorenz-like attractors
Gonchenko, SV
Ovsyannikov, II
Simó, C
Turaev, D
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2005, 15 (11): : 3493 - 3508
[2] On discrete Lorenz-like attractors in three-dimensional maps with axial symmetry
Gonchenko, Sergey
Gonchenko, Aleksandr
CHAOS, 2023, 33 (12)
[3] Examples of Lorenz-like Attractors in Henon-like Maps
Gonchenko, S. V.
Gonchenko, A. S.
Ovsyannikov, I. I.
Turaev, D. V.
MATHEMATICAL MODELLING OF NATURAL PHENOMENA, 2013, 8 (05) : 48 - 70
[4] On Global Bifurcations of Three-dimensional Diffeomorphisms Leading to Lorenz-like Attractors
Gonchenko, S. V.
Ovsyannikov, I. I.
MATHEMATICAL MODELLING OF NATURAL PHENOMENA, 2013, 8 (05) : 71 - 83
[5] On global bifurcations in three-dimensional diffeomorphisms leading to wild Lorenz-like attractors
S. V. Gonchenko
L. P. Shilnikov
D. V. Turaev
Regular and Chaotic Dynamics, 2009, 14
[6] On global bifurcations in three-dimensional diffeomorphisms leading to wild Lorenz-like attractors
Gonchenko, S. V.
Shilnikov, L. P.
Turaev, D. V.
REGULAR & CHAOTIC DYNAMICS, 2009, 14 (01): : 137 - 147
[7] Chaos Control and Synchronization in Fractional-Order Lorenz-Like System
Bhalekar, Sachin
INTERNATIONAL JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 2012
[8] The three-dimensional generalized Henon map: Bifurcations and attractors
Hampton, Amanda E. E.
Meiss, James D. D.
CHAOS, 2022, 32 (11)
[9] Attractors from one dimensional Lorenz-like maps
Choi, Y
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2004, 11 (2-3) : 715 - 730
[10] Studying Stochastic Resonance Phenomenon in the Fractional-Order Lorenz-Like Chaotic System
Zhou, Zuanbo
Yu, Wenxin
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2022, 32 (10):

← 1 2 3 4 5 →