Nonlinear Dynamics

, Volume 82, Issue 4, pp 2069–2079 | Cite as

A new six-term 3-D chaotic system with fan-shaped Poincaré maps

  • Jinmei Liu
  • Qiang Qu
  • Guanjing Li
Original Paper


A new three-dimensional chaotic system with fan-shaped Poincaré maps is proposed. Based on merely six terms, the system is easy to implement. Its dynamic behaviors, such as equilibrium points, Poincaré maps, power spectra, Lyapunov exponent spectra, bifurcation diagrams and forming mechanism, are analyzed theoretically and numerically. Results of theoretical analyses and numerical simulations indicate that the proposed system possesses complex chaotic attractors. Its equilibrium points are unstable, and the system can keep chaotic when its parameters vary in a wide domain. Furthermore, circuit simulations of the system are discussed. The results of numerical simulations and circuit simulations coincide very well. By virtue of its complex dynamic behaviors and wide-range parameters, the system can be adopted in some application fields where wide-range parameters and complex behaviors are usually preferred, such as secure communication, data encryption, information hiding.


Chaos Attractors Poincaré map Fan-shaped 



This work was supported by the National Natural Science Foundations of China (Nos. 21310018 and 61077030), the Science and Technology Research Program for the International Cooperation of Guangdong Province of China (2010B050900016). The authors are grateful to the reviewers for their valuable comments on the paper.


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.College of Information Science and TechnologyJinan UniversityGuangzhouChina
  2. 2.Automobile Electronic Technology DepartmentShandong Transport Vocational CollegeWeifangChina

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