Nonlinear Dynamics

, Volume 79, Issue 4, pp 2295–2308 | Cite as

Hyperchaos in a 4D memristive circuit with infinitely many stable equilibria

  • Qingdu LiEmail author
  • Hongzheng Zeng
  • Jing Li
Original Paper


This paper studies a four-dimensional (4D) memristive system modified from the 3D chaotic system proposed by Lü and Chen. The new system keeps the symmetry and dissipativity of the original system and has an uncountable infinite number of stable and unstable equilibria. By varying the strength of the memristor, we find rich complex dynamics, such as limit cycles, torus, chaos, and hyperchaos, which can peacefully coexist with the stable equilibria. To explain such coexistence, we compute the unstable manifolds of the equilibria, find that the manifolds create a safe zone for the hyperchaotic attractor, and also find many heteroclinic orbits. To verify the existence of hyperchaos in the 4D memristive circuit, we carry out a computer-assisted proof via a topological horseshoe with two-directional expansions, as well as a circuit experiment on oscilloscope views.


Chaos Hyperchaos Manifolds Topological horseshoe Memristive circuits 



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), and 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

  1. 1.Key Laboratory of Industrial Internet of Things and 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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