A Review of Fractional-Order Chaotic Systems of Memristive Neural Networks

Chunhua Wang (), Yufei Li, Gang Yang and Quanli Deng
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Chunhua Wang: College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China
Yufei Li: College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China
Gang Yang: 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

Mathematics, 2025, vol. 13, issue 10, 1-22

Abstract: At the end of the 20th century, the rapid development of brain-like dynamics was attributed to the excellent modeling of numerous neurons and neural systems, which effectively simulated biological behaviors observed in the human brain. With the continuous advancement of research, memristive neural networks (MNNs) have been extensively studied. In recent years, the exploration of fractional-order MNNs (FMNNs) has attracted research interest, leading to the discovery of the system’s dynamical phenomena, including transient chaos, hyperchaos, multi-stability, and the coexistence of attractors. To facilitate comparative research and learning, a review of the newly proposed fractional-order chaotic system models in recent years is urgently needed. In this review, we first introduce the basic theoretical knowledge of chaotic dynamics, artificial neural networks, fractional order, and memristors. Then, we mathematically describe the fractional-order systems and detail the highly regarded FMNNs in recent years, making comparative discussions and studies. Finally, we discuss the application of these models across diverse domains and propose thought-provoking questions and future research directions.

Keywords: chaos; chaotic system; fractional order; discrete-time neural network; memristor; dynamical behavior (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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