Dynamics of a new Lorenz-like chaotic system

被引:98
|
作者
Liu, Yongjian [1 ,2 ]
Yang, Qigui [1 ]
机构
[1] S China Univ Technol, Sch Math Sci, Guangzhou 510640, Guangdong, Peoples R China
[2] Yulin Normal Univ, Dept Math & Computat Sci, Yulin 537000, Peoples R China
基金
中国国家自然科学基金;
关键词
Chaotic system; Center manifold theorem; Degenerate pitchfork; Homoclinic orbit; Heteroclinic orbit; HOPF-BIFURCATION ANALYSIS; CHENS SYSTEM; CANONICAL FORM; LU SYSTEM; SYNCHRONIZATION; ATTRACTOR; STABILITY; EQUATION;
D O I
10.1016/j.nonrwa.2009.09.001
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The present work is devoted to giving new insights into a new Lorenz-like chaotic system. The local dynamical entities, such as the number of equilibria, the stability of the hyperbolic equilibria and the stability of the non-hyperbolic equilibrium obtained by using the center manifold theorem, the pitchfork bifurcation and the degenerate pitchfork bifurcation, Flopf bifurcations and the local manifold character, are all analyzed when the parameters are varied in the space of parameters. The existence of homoclinic and heteroclinic orbits of the system is also rigorously studied. More exactly, for b >= 2a > 0 and c > 0, we prove that the system has no homoclinic orbit but has two and only two heteroclinic orbits. (C) 2009 Elsevier Ltd. All rights reserved.
引用
收藏
页码:2563 / 2572
页数:10
相关论文
共 50 条
  • [31] Delay Feedback Control of the Lorenz-Like System
    Chen, Qin
    Gao, Jianguo
    MATHEMATICAL PROBLEMS IN ENGINEERING, 2018, 2018
  • [32] DYNAMICS OF A GENERALIZED LORENZ-LIKE CHAOS DYNAMICAL SYSTEMS
    Zhang, Fuchen
    Zhou, Ping
    Qin, Jin
    Mu, Chunlai
    Xu, Fei
    JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2021, 11 (03): : 1577 - 1587
  • [33] HOPF BIFURCATION AND NEW SINGULAR ORBITS COINED IN A LORENZ-LIKE SYSTEM
    Wang, Haijun
    Li, Xianyi
    JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2018, 8 (05): : 1307 - 1325
  • [34] From wild Lorenz-like to wild Rovella-like dynamics
    Hittmeyer, Stefanie
    Krauskopf, Bernd
    Osinga, Hinke M.
    DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, 2015, 30 (04): : 525 - 542
  • [35] Cryptanalysis of Image Encryption Algorithm Based on Fractional-Order Lorenz-Like Chaotic System
    Ahmad, Musheer
    Khan, Imran Raza
    Alam, Shahzad
    EMERGING ICT FOR BRIDGING THE FUTURE, VOL 2, 2015, 338 : 381 - 388
  • [36] A class of Lorenz-like systems
    Lainscsek, Claudia
    CHAOS, 2012, 22 (01)
  • [37] Octonionic Lorenz-like condition
    Tanisli, Murat
    Jancewicz, Bernard
    PRAMANA-JOURNAL OF PHYSICS, 2012, 78 (02): : 165 - 174
  • [38] A Unified Lorenz-Like System and Its Tracking Control
    Li Chun-Lai
    Zhao Yi-Bo
    COMMUNICATIONS IN THEORETICAL PHYSICS, 2015, 63 (03) : 317 - 324
  • [39] Symmetry-Break in a Minimal Lorenz-Like System
    Lucarini, Valerio
    Fraedrich, Klaus
    CHAOTIC SYSTEMS: THEORY AND APPLICATIONS, 2010, : 170 - +
  • [40] Octonionic Lorenz-like condition
    MURAT TANIŞLI
    BERNARD JANCEWICZ
    Pramana, 2012, 78 : 165 - 174