Nonlinear Dynamics

, Volume 81, Issue 3, pp 1275–1288 | Cite as

A four-wing hyper-chaotic attractor generated from a 4-D memristive system with a line equilibrium

  • Jian MaEmail author
  • Zengqiang Chen
  • Zhonglin Wang
  • Qing Zhang
Original Paper


A new hyper-chaotic system is presented in this paper by adding a smooth flux-controlled memristor and a cross-product item into a three-dimensional autonomous chaotic system. It is exciting that this new memristive system can show a four-wing hyper-chaotic attractor with a line equilibrium. The dynamical behaviors of the proposed system are analyzed by Lyapunov exponents, bifurcation diagram and Poincaré maps. Then, by using the topological horseshoe theory and computer-assisted proof, the existence of hyperchaos in the system is verified theoretically. Finally, an electronic circuit is designed to implement the hyper-chaotic memristive system.


Hyperchaos Four-wing attractor A line equilibrium Memristor Topological horseshoe 



This work is partially supported by Natural Science Foundation of China Grants No. 61174094, Tianjin Nature Science Foundation Grant No. 14JCYBJC18700 and Shandong Provincial Natural Science Foundation Grant No. ZR2012FM034.


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Jian Ma
    • 1
    • 2
    Email author
  • Zengqiang Chen
    • 1
    • 3
  • Zhonglin Wang
    • 2
  • Qing Zhang
    • 3
  1. 1.College of Computer and Control EngineeringNankai UniversityTianjinChina
  2. 2.Department of Physics and ElectronicsBinzhou UniversityBinzhouChina
  3. 3.College of ScienceCivil Aviation University of ChinaTianjinChina

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