Nonlinear Dynamics

, Volume 60, Issue 3, pp 443–457 | Cite as

A new type of four-wing chaotic attractors in 3-D quadratic autonomous systems

  • Zenghui Wang
  • Guoyuan Qi
  • Yanxia Sun
  • Barend Jacobus van Wyk
  • Michaël Antonie van Wyk
Original Paper


In this paper, several smooth canonical 3-D continuous autonomous systems are proposed in terms of the coefficients of nonlinear terms. These systems are derived from the existing 3-D four-wing smooth continuous autonomous chaotic systems. These new systems are the simplest chaotic attractor systems which can exhibit four wings. They have the basic structure of the existing 3-D four-wing systems, which means they can be extended to the existing 3-D four-wing chaotic systems by adding some linear and/or quadratic terms. Two of these systems are analyzed. Although the two systems are similar to each other in structure, they are different in dynamics. One is sensitive to the initializations and sampling time, but another is not, which is shown by comparing Lyapunov exponents, bifurcation diagrams, and Poincaré maps.

Chaos Four-wing chaotic attractor Lyapunov exponents Bifurcation Poincaré map 


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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Zenghui Wang
    • 1
    • 2
  • Guoyuan Qi
    • 1
  • Yanxia Sun
    • 1
  • Barend Jacobus van Wyk
    • 1
  • Michaël Antonie van Wyk
    • 1
  1. 1.French South African Technical Institute in Electronics (F’SATIE) & Department of Electrical EngineeringTshwane University of TechnologyPretoriaSouth Africa
  2. 2.Department of AutomationShandong University of Science and TechnologyQingaoChina

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