Dynamical behaviors, control and synchronization of a new chaotic model with complex variables and cubic nonlinear terms

被引：24
作者：
Mahmoud, Emad E. [1 ,2 ]
Al-Adwani, Madeha A. [2 ]
机构：
[1] Sohag Univ, Fac Sci, Dept Math, Sohag 82524, Egypt
[2] Taif Univ, Fac Sci, Dept Math, At Taif, Saudi Arabia
来源：
RESULTS IN PHYSICS | 2017年 / 7卷
关键词：
Chaotic; Control; Synchronization; Lyapunov stability; Complex; LAG SYNCHRONIZATION; ACTIVE CONTROL; SYSTEMS; EQUATIONS;
D O I：
10.1016/j.rinp.2017.02.039
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
A novel chaotic model with complex variables and cubic non-linear terms was proposed. The new system is a six dimensional continuous real autonomous chaotic system. The characteristics of this system containing invariance, dissipation, equilibria and their stability, Lyapunov exponents, Lyapunov dimension, bifurcation diagrams and chaotic achievement are studied. Converting and turning the system chaotic behavior to its unstable trivial fixed point via the Lyapunov stability theorem. An approach proposed to analyze the system chaos synchronization. Analytical expressions are derived for control functions. The chaos synchronization results were employed to develop a simple application in secure communication. Numerical effects computed to experiment the control forces scientific expressions gravity and to show the chaos synchronization of a chaotic system. (C) 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license
引用
收藏
页码：1346 / 1356
页数：11
相关论文
共 30 条
  • [1] Analytical and Numerical Study of the Projective Synchronization of the Chaotic Complex Nonlinear Systems with Uncertain Parameters and Its Applications in Secure Communication
    Abualnaja, Kholod M.
    Mahmoud, Emad E.
    [J]. MATHEMATICAL PROBLEMS IN ENGINEERING, 2014, 2014
  • [2] Global chaos synchronization of new chaotic systems via nonlinear control
    Chen, HK
    [J]. CHAOS SOLITONS & FRACTALS, 2005, 23 (04) : 1245 - 1251
  • [3] Synchronization of an uncertain unified chaotic system via adaptive control
    Chen, SH
    Lü, JH
    [J]. CHAOS SOLITONS & FRACTALS, 2002, 14 (04) : 643 - 647
  • [4] THE REAL AND COMPLEX LORENZ EQUATIONS AND THEIR RELEVANCE TO PHYSICAL SYSTEMS
    FOWLER, AC
    GIBBON, JD
    MCGUINNESS, MJ
    [J]. PHYSICA D, 1983, 7 (1-3): : 126 - 134
  • [5] THE COMPLEX LORENTZ EQUATIONS
    FOWLER, AC
    GIBBON, JD
    MCGUINNESS, MJ
    [J]. PHYSICA D, 1982, 4 (02): : 139 - 163
  • [6] THE LIAPUNOV DIMENSION OF STRANGE ATTRACTORS
    FREDERICKSON, P
    KAPLAN, JL
    YORKE, ED
    YORKE, JA
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1983, 49 (02) : 185 - 207
  • [7] Synchronization of two different systems by using generalized active control
    Ho, MC
    Hung, YC
    [J]. PHYSICS LETTERS A, 2002, 301 (5-6) : 424 - 428
  • [8] Khalil H. K., 1992, NONLINEAR SYSTEM
  • [9] Asynchronous anti-noise hyper chaotic secure communication system based on dynamic delay and state variables switching
    Liu, Hongjun
    Wang, Xingyuan
    Zhu, Quanlong
    [J]. PHYSICS LETTERS A, 2011, 375 (30-31) : 2828 - 2835
  • [10] LORENZ EN, 1963, J ATMOS SCI, V20, P130, DOI 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO
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