The European Physical Journal Special Topics

, Volume 228, Issue 10, pp 1995–2009 | Cite as

Extreme multistability in memristive hyper-jerk system and stability mechanism analysis using dimensionality reduction model

  • Yunzhen Zhang
  • Zhong Liu
  • Huagan Wu
  • Shengyao Chen
  • Bocheng BaoEmail author
Regular Article
Part of the following topical collections:
  1. Memristor-based Systems: Nonlinearity, Dynamics and Applications


This paper presents a memristive hyper-jerk system with smooth hyperbolic tangent memductance nonlinearity. Such a smooth memductance nonlinearity can cause the system to possess a line equilibrium therein, leading to the emergence of extreme multistability with coexisting infinitely many attractors due to the existence of a zero eigenvalue. To illustrate the stability mechanism, the dimensionality reduction model of the memristive hyper-jerk system is obtained using state variable mapping (SVM) method and several isolated equilibria are yielded from the dimensionality reduction model. As a consequence, the initial-dependent extreme multistability in the memristive hyper-jerk system is converted into the initial-related parameter-dependent dynamics in the dimensionality reduction model and the stability mechanism analysis is thereby executed. Furthermore, PSIM circuit simulations based on a physical circuit are performed to confirm the coexisting infinitely many attractors.


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Copyright information

© EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Yunzhen Zhang
    • 1
  • Zhong Liu
    • 1
  • Huagan Wu
    • 2
  • Shengyao Chen
    • 1
  • Bocheng Bao
    • 2
    Email author
  1. 1.Department of Electronic EngineeringNanjing University of Science and TechnologyNanjingP.R. China
  2. 2.School of Information Science and Engineering, Changzhou UniversityChangzhouP.R. China

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