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

Research output: Contribution to journalArticlepeer-review

29 Citations (Scopus)


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 fourwing 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.

Original languageEnglish
Pages (from-to)443-457
Number of pages15
JournalNonlinear Dynamics
Issue number3
Publication statusPublished - May 2010
Externally publishedYes


  • Bifurcation
  • Chaos
  • Four-wing chaotic attractor
  • Lyapunov exponents
  • Poincaré map

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Applied Mathematics
  • Electrical and Electronic Engineering


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