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A Review of Chaotic Systems Based on Memristive Hopfield Neural Networks

Author

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  • Hairong Lin

    (College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China)

  • Chunhua Wang

    (College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China)

  • Fei Yu

    (School of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha 410114, China)

  • Jingru Sun

    (College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China)

  • Sichun Du

    (College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China)

  • Zekun Deng

    (College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China)

  • Quanli Deng

    (College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China)

Abstract

Since the Lorenz chaotic system was discovered in 1963, the construction of chaotic systems with complex dynamics has been a research hotspot in the field of chaos. Recently, memristive Hopfield neural networks (MHNNs) offer great potential in the design of complex, chaotic systems because of their special network structures, hyperbolic tangent activation function, and memory property. Many chaotic systems based on MHNNs have been proposed and exhibit various complex dynamical behaviors, including hyperchaos, coexisting attractors, multistability, extreme multistability, multi-scroll attractors, multi-structure attractors, and initial-offset coexisting behaviors. A comprehensive review of the MHNN-based chaotic systems has become an urgent requirement. In this review, we first briefly introduce the basic knowledge of the Hopfiled neural network, memristor, and chaotic dynamics. Then, different modeling methods of the MHNN-based chaotic systems are analyzed and discussed. Concurrently, the pioneering works and some recent important papers related to MHNN-based chaotic systems are reviewed in detail. Finally, we survey the progress of MHNN-based chaotic systems for application in various scenarios. Some open problems and visions for the future in this field are presented. We attempt to provide a reference and a resource for both chaos researchers and those outside the field who hope to apply chaotic systems in a particular application.

Suggested Citation

  • Hairong Lin & Chunhua Wang & Fei Yu & Jingru Sun & Sichun Du & Zekun Deng & Quanli Deng, 2023. "A Review of Chaotic Systems Based on Memristive Hopfield Neural Networks," Mathematics, MDPI, vol. 11(6), pages 1-18, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1369-:d:1094547
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