A generalized 3-d four-wing chaotic system

Zenghui Wang, Guoyuan Qi, Yanxia Sun, Michaël Antonie Van Wyk, Barend Jacobus Van Wyk

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


In this paper, several three-dimensional (3-D) four-wing smooth quadratic autonomous chaotic systems are analyzed. It is shown that these systems have similar features. A simpler and generalized 3-D continuous autonomous system is proposed based on these features which can be extended to existing 3-D four-wing chaotic systems by adding some linear and/or quadratic terms. The new system can generate a four-wing chaotic attractor with simple topological structures. Some basic properties of the new system is analyzed by means of Lyapunov exponents, bifurcation diagrams and Poincaré maps. Phase diagrams show that the equilibria are related to the existence of multiple wings.

Original languageEnglish
Pages (from-to)3841-3853
Number of pages13
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Issue number11
Publication statusPublished - Nov 2009
Externally publishedYes


  • Bifurcation
  • Chaos
  • Four-wing chaos
  • Lyapunov exponents

ASJC Scopus subject areas

  • Modeling and Simulation
  • Engineering (miscellaneous)
  • Multidisciplinary
  • Applied Mathematics


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