A novel bounded 4D chaotic system

被引：31
作者：
Zhang, Jianxiong [1 ]
Tang, Wansheng [1 ]
机构：
[1] Tianjin Univ, Inst Syst Engn, Tianjin 300072, Peoples R China
来源：
NONLINEAR DYNAMICS | 2012年 / 67卷 / 04期
基金：
中国国家自然科学基金; 高等学校博士学科点专项科研基金;
关键词：
Hyperchaos; Ultimate bound; Positively invariant set; Lyapunov function; LORENZ SYSTEM; ATTRACTORS; SET;
D O I：
10.1007/s11071-011-0159-3
中图分类号：
TH [机械、仪表工业];
学科分类号：
0802 ;
摘要：
This paper presents a novel bounded four-dimensional (4D) chaotic system which can display hyperchaos, chaos, quasiperiodic and periodic behaviors, and may have a unique equilibrium, three equilibria and five equilibria for the different system parameters. Numerical simulation shows that the chaotic attractors of the new system exhibit very strange shapes which are distinctly different from those of the existing chaotic attractors. In addition, we investigate the ultimate bound and positively invariant set for the new system based on the Lyapunov function method, and obtain a hyperelliptic estimate of it for the system with certain parameters.
引用
收藏
页码：2455 / 2465
页数：11
相关论文
共 24 条
  • [1] Yet another chaotic attractor
    Chen, GR
    Ueta, T
    [J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 1999, 9 (07): : 1465 - 1466
  • [2] A novel hyperchaos system only with one equilibrium
    Chen, Zengqiang
    Yang, Yong
    Qi, Guoyuan
    Yuan, Zhuzhi
    [J]. PHYSICS LETTERS A, 2007, 360 (06) : 696 - 701
  • [3] Analysis of a new 3D smooth autonomous system with different wing chaotic attractors and transient chaos
    Dadras, Sara
    Momeni, Hamid Reza
    Qi, Guoyuan
    [J]. NONLINEAR DYNAMICS, 2010, 62 (1-2) : 391 - 405
  • [4] Generating one-, two-, three- and four-scroll attractors from a novel four-dimensional smooth autonomous chaotic system
    Dadras, Sara
    Momeni, Hamid Reza
    [J]. CHINESE PHYSICS B, 2010, 19 (06)
  • [5] Four-scroll hyperchaos and four-scroll chaos evolved from a novel 4D nonlinear smooth autonomous system
    Dadras, Sara
    Momeni, Hamid Reza
    [J]. PHYSICS LETTERS A, 2010, 374 (11-12) : 1368 - 1373
  • [6] LEFCHETZ S, 1963, DIFFERENTIAL EQUATIO
  • [7] Bounds for attractors and the existence of homoclinic orbits in the Lorenz system
    Leonov, GA
    [J]. PMM JOURNAL OF APPLIED MATHEMATICS AND MECHANICS, 2001, 65 (01): : 19 - 32
  • [8] Estimating the ultimate bound and positively invariant set for the Lorenz system and a unified chaotic system
    Li, Damei
    Lu, Jun-an
    Wu, Xiaoqun
    Chen, Guanrong
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 323 (02) : 844 - 853
  • [9] LORENZ EN, 1963, J ATMOS SCI, V20, P130, DOI 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO
  • [10] 2
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