[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83631-en":3,"doc-seo-83631-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},83631,1649267921044,"Ava Thompson","https://us-avatar.wpscdn.com/avatar/1800007509477c92dfb?_k=1782875107921204101",6,"Technology","Electronic Bursting Neuron Design Equations and Hardware Implementation","Electronic bursting neuron circuits enable spiking neural networks for neuroprosthetics, artificial memory, and real-time intensive calculations. Existing electronic neuron schemes often trade off simplicity, cost, achievable dynamical regimes, or mathematical completeness. This study presents a new bursting electronic neuron design as a circuit realization of phase-locked loop equations. A hybrid workflow starts from phenomenological equations, then adjusts and simplifies them for practical analog hardware implementation without directly embedding biophysical equations. The resulting circuit remains implementation-friendly and extends naturally from a single neuron to small neural circuits.","arXiv :2607 .02 122v 1 [ cs .NE] 2 Jul 2026  \nElectronic Bursting Neuron: design, equations and hardware implementation  \nLev V. Takaishvili 1,2 , Vladimir I. Ponomarenko2,3 , Maksim V. Kornilov 1,2 , Ilya V. Sysoev 1,2  \n1 Peter the Great St. Petersburg Polytechnic University, Russia;  \n3 Saratov State University, Russia;  \n2 Saratov Branch of Kotelnikov Institute of Radioengineering and Electronics  \nof RAS, Russia  \nAbstract  \nElectronic neurons are a keystone for construction of the spiking neural networks which have numerous applications in neuroprosthetics, artificial memory, intensive calculations etc. A number of concepts of electronic neurons has been already proposedm with some of them implemented in hardware. However, new schemes are of significant interest since the existing ones do not fit all requirements: either they are too complex and expensive in realization, or they are not able to demonstrate all demanded regimes, or their do not have a appropriate mathematical description and therefore maybe investigated only experimentally etc.  \nIn this study we propose a new design of bursting electronic neuron constructed as a circuit implementation of the equations of a phase-locked loop system. To succeed, we use a novel hybrid approach: we start from the phenomenological equations providing the demanded, then we adjust and modify these equations to simplify the implementation rather than implementing the biophysical equations into thee hardware directly or writing equations for the already constructed circuit. The resulting circuit is simple in implementation and well matches the underlying equations. It can be used for description of not only a single neuron, but small neural circuits too.  \n1 Introduction  \nModeling dynamic processes in neural systems remains one of the central tasks of modern computational neuroscience and nonlinear dynamics. Classical models such as the HodgkinHuxley model [1] and the FitzHugh-Nagumo model [2, 3] laid the foundation for understanding the mechanisms of nerve impulse generation and transmission. At the same time, the researchers are still looking for new physically realizable models capable of reproducing complex modes of neural activity, including chaotic and periodic oscillations [4, 5] . Electronic analogues of neurons are of particular interest. They can be implemented as hardware circuits for creating neuromorphic systems and hardware neural networks [6, 7] . This approach allows us to explore the dynamics of neurons in real time and overcome the computational limitations of purely software simulations [8, 9] . Switching from abstract mathematical models to the real world implementations is especially important for tasks of synchronization, signal processing, and studying the collective dynamics of neural ensembles [10, 11] .  \nA number of hardware implementations of the the electronic concept have been already proposed, with most of them realizing the idea of direct modeling the biophysical equations for transmembrane current starting from the pioneering works by [12, 13, 14] and further implementations of FitzHugh–Nagumo model [15, 16, 17, 18], Morris–Lecar model [19] and different, mostly reduced and simplified versions of Hodgkin–Huxley model [20, 21, 22] .  \nAn alternative way is to find a mathamatical model or develop an electronic circuit, which demonstrates spiking and bursting phenomenologically without clear biophysical background. Here, we construct a hardware generator based on the ideas from [23, 24, 25] . In the paper by [23] the authors found the neuron-like modes in the equations of a generator proposed much earlier by [26] . The equations described a model of a phase-locked loop system with three dynamic variables, one of which — the voltage y might be matched with a trans-membrane voltage. The hardware implementation of this system [25] is more complex, containing, in addition to these equations, a voltage-controlled generator (VCG) and a phase detector.  \nI","cbCais5ujipIxz4b","https://ap.wps.com/l/cbCais5ujipIxz4b","pdf",2836472,1,13,"English","en",105,"# Introduction\n# Mathematical model","[{\"question\":\"What is the main goal of the proposed electronic bursting neuron design?\",\"answer\":\"To develop a new analog circuit that generates bursting neuron dynamics by realizing equations derived from a phase-locked loop system, while avoiding complexity, expense, and implementation difficulties found in prior schemes.\"},{\"question\":\"How does the study handle practical implementation challenges in the original phase-locked-loop-based model?\",\"answer\":\"It introduces a method to limit the phase variable growth (so it does not increase indefinitely) and replaces the hard-to-build nonlinear cosine term with a simpler hyperbolic tangent function.\"},{\"question\":\"What role does the hybrid approach play in constructing the hardware circuit?\",\"answer\":\"The method begins with phenomenological equations that match the desired behaviors, then modifies them specifically to simplify circuit implementation rather than directly translating biophysical equations into hardware.\"}]",1784189391,33,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"electronic-bursting-neuron-design-equations-and-hardware-implementation","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/technology/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/electronic-bursting-neuron-design-equations-and-hardware-implementation/83631/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What is the main goal of the proposed electronic bursting neuron design?","Question",{"text":75,"@type":76},"To develop a new analog circuit that generates bursting neuron dynamics by realizing equations derived from a phase-locked loop system, while avoiding complexity, expense, and implementation difficulties found in prior schemes.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the study handle practical implementation challenges in the original phase-locked-loop-based model?",{"text":80,"@type":76},"It introduces a method to limit the phase variable growth (so it does not increase indefinitely) and replaces the hard-to-build nonlinear cosine term with a simpler hyperbolic tangent function.",{"name":82,"@type":73,"acceptedAnswer":83},"What role does the hybrid approach play in constructing the hardware circuit?",{"text":84,"@type":76},"The method begins with phenomenological equations that match the desired behaviors, then modifies them specifically to simplify circuit 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