Nonlinear Dynamics

, Volume 59, Issue 3, pp 515–527 | Cite as

A four-wing hyper-chaotic attractor and transient chaos generated from a new 4-D quadratic autonomous system

Original Paper


This paper presents a new four-dimensional (4-D) smooth quadratic autonomous chaotic system, which can present periodic orbit, chaos, and hyper-chaos under the conditions on different parameters. Importantly, the system can generate a four-wing hyper-chaotic attractor and a pair of coexistent double-wing hyper-chaotic attractors with two symmetrical initial conditions. Furthermore, a four-wing transient chaos occurs in the system. The dynamic analysis approach- in the paper involves time series, phase portraits, Poincaré maps, bifurcation diagrams, and Lyapunov exponents, to investigate some basic dynamical behaviors of the proposed 4-D system.


Chaos Hyper-chaos Four-wing attractor Transient chaos 


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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.F’SATIE and Department of Electrical EngineeringTshwane University of TechnologyPretoriaSouth Africa
  2. 2.Department of Industry DesignTianjin University of Science and TechnologyTianjinP.R. China
  3. 3.Department of AutomationNankai UniversityTianjinP.R. China

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