A Review of Chaotic Systems Based on Memristive Hopfield Neural Networks

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.

Automated summary

Since the discovery of the Lorenz chaotic system in 1963, the construction of chaotic systems with complex dynamics has been a hot topic in chaos research. Recently, memristive Hopfield neural networks (MHNNs) have shown great potential in designing complex, chaotic systems due to their unique network structures, hyperbolic tangent activation function, and memory property. This review provides an analysis of different modeling methods, reviews pioneering works and recent important papers, and surveys the progress of MHNN-based chaotic systems in various applications. It aims to be a reference and resource for both chaos researchers and those interested in applying chaotic systems.