https://doi.org/10.1140/epjp/s13360-026-07839-7
Regular Article
Design of a fractional-order discrete memristive spiking neuron model and its information processing mechanism
1
School of Automation and Electronic Information, Xiangtan University, 411105, Xiangtan, Hunan, China
2
Department of Neurobiology, School of Basic Medical Sciences; Key Laboratory of Major Brain Disease and Aging Research (Ministry of Education), Chongqing Medical University, 400083, Chongqing, China
3
School of Life and Health Information Science and Engineering, Chongqing University of Posts and Telecommunications, 400065, Chongqing, China
a
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b
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Received:
4
March
2026
Accepted:
16
May
2026
Published online:
31
May
2026
Abstract
Neuromorphic computing aims to emulate the brain’s efficient information processing mechanisms, with spiking neural networks (SNNs) as a core framework. However, emulating complex biological dynamics—such as synaptic plasticity, memory decay, and multi-dimensional signal processing—remains a critical challenge. This study proposes a spiking neuron model using a fractional-order discrete memristor and investigates its information processing applications. Based on the G-L fractional-order difference definition, a fractional-order discrete memristor is designed, which exhibits rapid memory decay and asymptotic stability, verified via Z-transform and Jury’s criterion. Integrated into a discrete Izhikevich neuron, the memristive spiking neuron can process multi-channel spike inputs and dynamically adjust internal weights. A spike-driven ring-coupled network is also constructed, and four synchronization metrics are defined to quantify spiking synchrony. Simulations reveal that the network achieves higher synchronization under serial topology and external input. Finally, the filtering function and information feature extraction function of the designed discrete memristor were discussed. Meanwhile, the design scheme of discrete memristor with STDP function and the future implementation path of digital circuits were briefly explored. This work bridges fractional calculus, memristors, and neural information processing, offering a new framework for spiking neural networks with potential applications in signal filtering, feature extraction, and synchronous control, thereby enriching the theory of discrete fractional-order devices and supporting brain-inspired computing.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
