[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83240-en":3,"doc-seo-83240-105":30,"detail-sidebar-cat-0-en-105":90},{"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":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},83240,962075114101,"Seraphina","https://ap-avatar.wpscdn.com/avatar/e000253a75eb197efd?x-image-process=image/resize,m_fixed,w_180,h_180&k=1780044092746381165",8,"Research & Report","Single-Entity Spiking Neuron Models Survey","Survey paper on mathematical modeling of biologically plausible spiking neural systems, focusing specifically on single-entity (single-compartment) models. The work reviews and classifies neuron models and related components by shared features and application-oriented use cases, including spiking approaches and discrete or continuous analogs used to simulate biological dynamics such as membrane potential evolution. Emphasis is placed on comparing model properties and analyzing the problem domains they address, selecting approaches based on prevalence and novel perspectives.","Single-Entity Spiking Neuron Models: Survey  \nLeon Parepko  \nInnopolis University Innopolis, Russia [leonparerpko@gmail.com](leonparerpko@gmail.com)  \nDanila Shulepin  \nInnopolis University Innopolis, Russia [dshulepin2013@gmail.com](dshulepin2013@gmail.com)  \nAlbert Nasybullin  \nInnopolis University Innopolis, Russia [levshaazz@gmail.com](levshaazz@gmail.com)  \narXiv :2607 .07429v 1 [ cs .NE] 8 Jul 2026  \nAbstract—In this work, we reviewed different approaches in mathematical modeling of biologically plausible neural systems. Models are characterized and classified based on their common features and special use cases. In addition to spiking models, different types of discrete and continuous analogs are considered to accurately simulate biological processes, including membrane potential dynamics. The models under investigation include neurons and various components encountered in neural systems and affected the dynamics. The selection of specific approaches was driven by their prevalence and innovative perspectives in order to enhance the relevance of the presented information.  \nIndex Terms—neuroscience, dynamic systems, spiking neural network, biologically plausible, mathematical modeling  \nI. INTRODUCTION  \nThe study of the brain functioning remains a complex problem. While the first and second generations of artificial neural networks (ANNs), based on McCulloch-Pitts model [1] with different activation functions, could not provide the accurate simulation of all the concepts, including the time-dependent voltage dynamics, underlie biological neural networks [2] . Large-scale brain models have emerged as a potential solution. Among these models, spiking neural networks (the third generation of ANNs) have shown promising results [2] . However, the challenge lies in accurately distinguishing between these models and selecting the most appropriate one, given the current lack of robust classification methods.  \nIn stark contrast to similar works [2,16], the present paper aims to explicate the underlying principles of various approaches and provide a multifaceted survey that includes a models features comparison and an analysis of the correlated problems that these ones solve.  \nIn order to achieve this goal, we have categorized all neural systems models into two major sets: single-entity models, which are also referred to as single compartmental models; and composite models, or multi-compartmental models [3] . Nonetheless, we shall focus solely on the former class in this paper while providing a comprehensive classification of both categories in future work.  \nIn the context of single-entity models, a single computational unit initially represents the cell, which is described by a mathematical model. It ought to be noted that such models may comprise multiple equations. The key distinction here is that cell is not constructively divided into separate components (e.g., axon, dendrites, synapses), as is done in multicompartmental modeling, where each component corresponds to a distinct mathematical model.  \nII. INTEGRATE AND FIRE MODELS  \nThe Integrate and Fire (IF) [4,5] is a collection of biophysically meaningless models, characterized by ordinary differential equations (ODEs) . The ones rely on two fundamental concepts: integration - summation of input signals, and firing - emitting a spike beyond a particular threshold Vth. These models are low-dimensional and neglect ion-channel dynamics. Corresponding abstraction could be constructed by an electrical circuit, where the capacitor represents the passive membrane V. The basic IF model (1) aggregates the input current Iext and generates a spike as described above.  \n(Cif ~~d~~VdtV IVtexh,tthen V = Vreset (1)  \nAlternatively, the more practical leaky-IF (LIF) model (2), which involves a constant membrane leak through a resistor, is commonly used.  \n(~~d~~difVtV=≥IexVtthtghe(Vn0V) reset (2)  \nThe membrane capacity is denoted by C, V0 represents the resting potential, and g signifi","cbCaiqA3RIx8UtDC","https://ap.wps.com/l/cbCaiqA3RIx8UtDC","pdf",203142,2,1,4,"English","en",105,"# Introduction\n## Integrate and Fire Models\n## Hodgkin-Huxley Based Models","[{\"question\":\"What does the survey focus on regarding spiking neuron models?\",\"answer\":\"The survey concentrates on single-entity, also called single-compartmental, models rather than multi-compartmental composite models.\"},{\"question\":\"How are Integrate-and-Fire (IF) models characterized?\",\"answer\":\"IF models are described as low-dimensional abstractions using ODEs, combining input integration and firing when a threshold Vth is exceeded, while neglecting ion-channel dynamics.\"},{\"question\":\"What limitations do IF-based neurons have for biological simulations?\",\"answer\":\"They simplify activity by emitting binary spikes and do not represent membrane potential dynamics beyond the threshold, failing to capture detailed action-potential properties such as duration, amplitude, and shape.\"}]",1784186164,10,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":28},"single-entity-spiking-neuron-models-survey","",{"@graph":36,"@context":84},[37,52,67],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,47,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":20},"https://docshare.wps.com/document/","Document",{"item":48,"name":12,"@type":43,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":43,"position":22},"https://docshare.wps.com/document/single-entity-spiking-neuron-models-survey/83240/",{"url":51,"name":13,"@type":53,"author":54,"headline":13,"publisher":56,"fileFormat":59,"inLanguage":24,"description":14,"dateModified":60,"datePublished":61,"encodingFormat":59,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":55},"Person",{"url":41,"name":57,"@type":58},"DocShare","Organization","application/pdf","2026-07-24","2026-07-16",true,{"@type":64,"interactionType":65,"userInteractionCount":20},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"What does the survey focus on regarding spiking neuron models?","Question",{"text":74,"@type":75},"The survey concentrates on single-entity, also called single-compartmental, models rather than multi-compartmental composite models.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"How are Integrate-and-Fire (IF) models characterized?",{"text":79,"@type":75},"IF models are described as low-dimensional abstractions using ODEs, combining input integration and firing when a threshold Vth is exceeded, while neglecting ion-channel dynamics.",{"name":81,"@type":72,"acceptedAnswer":82},"What limitations do IF-based neurons have for biological simulations?",{"text":83,"@type":75},"They simplify activity by emitting binary spikes and do not represent membrane potential dynamics beyond the threshold, failing to capture detailed action-potential properties such as duration, amplitude, and 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