A Review of Fractional-Order Chaotic Systems of Memristive Neural Networks
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 n...
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MDPI AG
2025-05-01
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| Series: | Mathematics |
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| author | Chunhua Wang Yufei Li Gang Yang Quanli Deng |
| author_facet | Chunhua Wang Yufei Li Gang Yang Quanli Deng |
| author_sort | Chunhua Wang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-db209a7680e84ea0affd06bfe7382d8e |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-db209a7680e84ea0affd06bfe7382d8e2025-08-20T02:33:47ZengMDPI AGMathematics2227-73902025-05-011310160010.3390/math13101600A Review of Fractional-Order Chaotic Systems of Memristive Neural NetworksChunhua Wang0Yufei Li1Gang Yang2Quanli Deng3College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, ChinaCollege of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, ChinaCollege of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, ChinaCollege of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, ChinaAt 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.https://www.mdpi.com/2227-7390/13/10/1600chaoschaotic systemfractional orderdiscrete-time neural networkmemristordynamical behavior |
| spellingShingle | Chunhua Wang Yufei Li Gang Yang Quanli Deng A Review of Fractional-Order Chaotic Systems of Memristive Neural Networks Mathematics chaos chaotic system fractional order discrete-time neural network memristor dynamical behavior |
| title | A Review of Fractional-Order Chaotic Systems of Memristive Neural Networks |
| title_full | A Review of Fractional-Order Chaotic Systems of Memristive Neural Networks |
| title_fullStr | A Review of Fractional-Order Chaotic Systems of Memristive Neural Networks |
| title_full_unstemmed | A Review of Fractional-Order Chaotic Systems of Memristive Neural Networks |
| title_short | A Review of Fractional-Order Chaotic Systems of Memristive Neural Networks |
| title_sort | review of fractional order chaotic systems of memristive neural networks |
| topic | chaos chaotic system fractional order discrete-time neural network memristor dynamical behavior |
| url | https://www.mdpi.com/2227-7390/13/10/1600 |
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