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Keywords = memristive Hindmarsh-Rose model

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15 pages, 7159 KB  
Article
Discrete Memristive Hindmarsh-Rose Neural Model with Fractional-Order Differences
by Fatemeh Parastesh, Karthikeyan Rajagopal, Sajad Jafari and Matjaž Perc
Fractal Fract. 2025, 9(5), 276; https://doi.org/10.3390/fractalfract9050276 - 24 Apr 2025
Cited by 3 | Viewed by 842
Abstract
Discrete systems can offer advantages over continuous ones in certain contexts, particularly in terms of simplicity and reduced computational costs, though this may vary depending on the specific application and requirements. Recently, there has been growing interest in using fractional differences to enhance [...] Read more.
Discrete systems can offer advantages over continuous ones in certain contexts, particularly in terms of simplicity and reduced computational costs, though this may vary depending on the specific application and requirements. Recently, there has been growing interest in using fractional differences to enhance discrete models’ flexibility and incorporate memory effects. This paper examines the dynamics of the discrete memristive Hindmarsh-Rose model by integrating fractional-order differences. Our results highlight the complex dynamics of the fractional-order model, revealing that chaotic firing depends on both the fractional-order and magnetic strength. Notably, certain magnetic strengths induce a transition from periodic firing in the integer-order model to chaotic behavior in the fractional-order model. Additionally, we explore the dynamics of two coupled discrete systems, finding that electrical coupling leads to the synchronization of chaotic dynamics, while chemical coupling ultimately results in a quiescent state. Full article
(This article belongs to the Special Issue Advances in Fractional-Order Chaotic and Complex Systems)
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13 pages, 3034 KB  
Article
Coexisting Firing Patterns in an Improved Memristive Hindmarsh–Rose Neuron Model with Multi-Frequency Alternating Current Injection
by Mengjiao Wang, Jie Ding, Bingqing Deng, Shaobo He and Herbert Ho-Ching Iu
Micromachines 2023, 14(12), 2233; https://doi.org/10.3390/mi14122233 - 12 Dec 2023
Cited by 4 | Viewed by 2850
Abstract
With the development of memristor theory, the application of memristor in the field of the nervous system has achieved remarkable results and has bright development prospects. Flux-controlled memristor can be used to describe the magnetic induction effect of the neuron. Based on the [...] Read more.
With the development of memristor theory, the application of memristor in the field of the nervous system has achieved remarkable results and has bright development prospects. Flux-controlled memristor can be used to describe the magnetic induction effect of the neuron. Based on the Hindmarsh–Rose (HR) neuron model, a new HR neuron model is proposed by introducing a flux-controlled memristor and a multi-frequency excitation with high–low frequency current superimposed. Various firing patterns under single and multiple stimuli are investigated. The model can exhibit different coexisting firing patterns. In addition, when the memristor coupling strength changes, the multiple stability of the model is eliminated, which is a rare phenomenon. Moreover, an analog circuit is built to verify the numerical simulation results. Full article
(This article belongs to the Special Issue Novel Computing Architectures and Digital Circuit Designs Using Memristors and Memristive Systems, 2nd Edition)
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18 pages, 4310 KB  
Article
The Impact of Higher-Order Interactions on the Synchronization of Hindmarsh–Rose Neuron Maps under Different Coupling Functions
by Mahtab Mehrabbeik, Atefeh Ahmadi, Fatemeh Bakouie, Amir Homayoun Jafari, Sajad Jafari and Dibakar Ghosh
Mathematics 2023, 11(13), 2811; https://doi.org/10.3390/math11132811 - 22 Jun 2023
Cited by 13 | Viewed by 2115
Abstract
In network analysis, links depict the connections between each pair of network nodes. However, such pairwise connections fail to consider the interactions among more agents, which may be indirectly connected. Such non-pairwise or higher-order connections can be signified by involving simplicial complexes. The [...] Read more.
In network analysis, links depict the connections between each pair of network nodes. However, such pairwise connections fail to consider the interactions among more agents, which may be indirectly connected. Such non-pairwise or higher-order connections can be signified by involving simplicial complexes. The higher-order connections become even more noteworthy when it comes to neuronal network synchronization, an emerging phenomenon responsible for the many biological processes in real-world phenomena. However, involving higher-order interactions may considerably increase the computational costs. To confound this issue, map-based models are more suitable since they are faster, simpler, more flexible, and computationally more optimal. Therefore, this paper addresses the impact of pairwise and non-pairwise neuronal interactions on the synchronization state of 10 coupled memristive Hindmarsh–Rose neuron maps. To this aim, electrical, inner linking, and chemical synaptic functions are considered as two- and three-body interactions in three homogeneous and two heterogeneous cases. The results show that through chemical pairwise and non-pairwise synapses, the neurons achieve synchrony with the weakest coupling strengths. Full article
(This article belongs to the Section E: Applied Mathematics)
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