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

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