Nonlinear Dynamics

, Volume 78, Issue 4, pp 2517–2531 | Cite as

Local bifurcation analysis and ultimate bound of a novel 4D hyper-chaotic system

  • Jiezhi Wang
  • Qing Zhang
  • Zengqiang Chen
  • Hang Li
Original Paper


This paper presents a new four-dimensional smooth quadratic autonomous hyper-chaotic system which can generate novel two double-wing periodic, quasi-periodic and hyper-chaotic attractors. The Lyapunov exponent spectrum, bifurcation diagram and phase portrait are provided. It is shown that this system has a wide hyper-chaotic parameter. The pitchfork bifurcation and Hopf bifurcation are discussed using the center manifold theory. The ellipsoidal ultimate bound of the typical hyper-chaotic attractor is observed. Numerical simulations are given to demonstrate the evolution of the two bifurcations and show the ultimate boundary region.


Hyper-chaos Pitchfork bifurcation Hopf bifurcation Ultimate bound  



This work was partially supported by the National Natural Science Foundation of China through Grant No. 11102226, the Fundamental Research Funds for the Central Universities through Grant Nos. ZXH2010D011, ZXH2012B003 and ZXH2012K002 and the Scientific Research Foundation of Civil Aviation University of China through Grant No. 07QD05X.


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Jiezhi Wang
    • 1
  • Qing Zhang
    • 1
  • Zengqiang Chen
    • 1
    • 2
  • Hang Li
    • 3
  1. 1.College of ScienceCivil Aviation University of ChinaTianjin People’s Republic of China
  2. 2.Department of AutomationNankai UniversityTianjin People’s Republic of China
  3. 3.Economics and Management CollegeCivil Aviation University of ChinaTianjin  People’s Republic of China

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