Nonlinear Dynamics

, Volume 78, Issue 2, pp 1087–1099 | Cite as

On hyperchaos in a small memristive neural network

  • Qingdu Li
  • Song Tang
  • Hongzheng Zeng
  • Tingting Zhou
Original Paper


This paper studies a small Hopfield neural network with a memristive synaptic weight. We show that the previous stable network after one weight replaced by a memristor can exhibit rich complex dynamics, such as quasi-periodic orbits, chaos, and hyperchaos, which suggests that the memristor is crucial to the behaviors of neural networks and may play a significant role. We also prove the existence of a saddle periodic orbit, and then present computer-assisted verification of hyperchaos through a homoclinic intersection of the stable and unstable manifolds, which gives a positive answer to an interesting question that whether a 4D memristive system with a line of equilibria can demonstrate hyperchaos.


Hyperchaos Homoclinic intersection Small neural networks Memristor 



We are very grateful to the reviewers for their valuable comments and suggestions. This work is supported in part by the National Natural Science Foundation of China (61104150), Science Fund for Distinguished Young Scholars of Chongqing (cstc2013jcyjjq40001), and the Science and Technology Project of Chongqing Education Commission (KJ130517).


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Qingdu Li
    • 1
  • Song Tang
    • 1
  • Hongzheng Zeng
    • 2
  • Tingting Zhou
    • 1
  1. 1.Key Laboratory of Industrial Internet of Things & Networked Control of Ministry of EducationChongqing University of Posts and TelecommunicationsChongqingChina
  2. 2.Research Center of Analysis and Control for Complex SystemsChongqing University of Posts and TelecommunicationsChongqingChina

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