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

被引：13
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
    Aguila-Camacho, Norelys
    Duarte-Mermoud, Manuel A.
    Gallegos, Javier A.
    [J]. 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
    Boccaletti, S
    Kurths, J
    Osipov, G
    Valladares, DL
    Zhou, CS
    [J]. 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
    Cafagna, Donato
    Grassi, Giuseppe
    [J]. MATHEMATICAL PROBLEMS IN ENGINEERING, 2013, 2013
  • [7] Fractional-order systems without equilibria: The first example of hyperchaos and its application to synchronization
    Cafagna, Donato
    Grassi, Giuseppe
    [J]. CHINESE PHYSICS B, 2015, 24 (08)
  • [8] Chaos in a new fractional-order system without equilibrium points
    Cafagna, Donato
    Grassi, Giuseppe
    [J]. 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
    Chen, E.
    Min, Lequan
    Chen, Guanrong
    [J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2017, 27 (03):
  • [10] Chen E, 2017, INT J BIFURCAT CHAOS, V27, P1750
12345678