A fractional-order form of a system with stable equilibria and its synchronization

被引：15
作者：
Wang, Xiong [1 ]
Ouannas, Adel [2 ]
Viet-Thanh Pham [3 ]
Abdolmohammadi, Hamid Reza [4 ]
机构：
[1] Shenzhen Univ, Inst Adv Study, Shenzhen 518060, Guangdong, Peoples R China
[2] Univ Larbi Tebessi, Dept Math & Comp Sci, Tebessa 12002, Algeria
[3] Ton Duc Thang Univ, Modeling Evolutionary Algorithms Simulat & Artifi, Fac Elect & Elect Engn, Ho Chi Minh City, Vietnam
[4] Golpayegan Univ Technol, Dept Elect Engn, Golpayegan, Iran
来源：
ADVANCES IN DIFFERENCE EQUATIONS | 2018年
基金：
中国国家自然科学基金;
关键词：
chaos; equilibrium; hidden attractor; fractional order; synchronization; CHAOTIC AUTONOMOUS SYSTEM; SPROTT C SYSTEM; CIRCUIT-DESIGN; PROJECTIVE SYNCHRONIZATION; LYAPUNOV FUNCTIONS; DYNAMICAL ANALYSIS; HIDDEN ATTRACTORS; MULTISTABILITY; IMPLEMENTATION; STABILITY;
D O I：
10.1186/s13662-018-1479-0
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
There has been an increasing interest in studying fractional-order chaotic systems and their synchronization. In this paper, the fractional-order form of a system with stable equilibrium is introduced. It is interesting that such a three-dimensional fractional system can exhibit chaotic attractors. Full-state hybrid projective synchronization scheme and inverse full-state hybrid projective synchronization scheme have been designed to synchronize the three-dimensional fractional system with different four-dimensional fractional systems. Numerical examples have verified the proposed synchronization schemes.
引用
收藏
页数：13
相关论文
共 75 条
[1]   Lyapunov functions for fractional order systems [J].
Aguila-Camacho, Norelys ;
Duarte-Mermoud, Manuel A. ;
Gallegos, Javier A. .
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2014, 19 (09) :2951-2957
[2]  
[Anonymous], 1994, Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, DOI 9780738204536
[3]  
[Anonymous], 1999, FRACTIONAL DIFFERENT
[4]   The synchronization of chaotic systems [J].
Boccaletti, S ;
Kurths, J ;
Osipov, G ;
Valladares, DL ;
Zhou, CS .
PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS, 2002, 366 (1-2) :1-101
[5]  
Cafagna D, 2013, MATH PROBL ENG, P380
[6]   Elegant Chaos in Fractional-Order System without Equilibria [J].
Cafagna, Donato ;
Grassi, Giuseppe .
MATHEMATICAL PROBLEMS IN ENGINEERING, 2013, 2013
[7]   Fractional-order systems without equilibria: The first example of hyperchaos and its application to synchronization [J].
Cafagna, Donato ;
Grassi, Giuseppe .
CHINESE PHYSICS B, 2015, 24 (08)
[8]   Chaos in a new fractional-order system without equilibrium points [J].
Cafagna, Donato ;
Grassi, Giuseppe .
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2014, 19 (09) :2919-2927
[9]   Discrete Chaotic Systems with One-Line Equilibria and Their Application to Image Encryption [J].
Chen, E. ;
Min, Lequan ;
Chen, Guanrong .
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2017, 27 (03)
[10]  
Chen E, 2017, INT J BIFURCAT CHAOS, V27, P1750
12345678