A Nearly Exact Discretization of a Two-Neuron System with a Time Delay

A Nearly Exact Discretization of a Two-Neuron System with a Time Delay | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article A Nearly Exact Discretization of a Two-Neuron System with a Time Delay A. M. A. Abo-Bakr This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6283929/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 29 Jul, 2025 Read the published version in Boundary Value Problems → Version 1 posted 9 You are reading this latest preprint version Abstract Delay differential equations (DDEs) play a crucial role in modeling dynamical systems where the future state depends on both the present and past values. These equations arise in various scientific fields, including neuroscience, engineering, and economics. However, their numerical discretization is challenging, as standard methods often fail to preserve essential properties such as stability and bifurcation behavior. This study applies the nearly exact discretization scheme (NEDS) to a two-neuron system with time delay, converting it into a 2m-dimensional discrete-time model while maintaining its key dynamical features. We conduct a detailed theoretical analysis of local stability and Neimark–Sacker bifurcation to gain insights into the system’s behavior. Additionally, we introduce a simplified hybrid control method to stabilize the discretized system, providing an efficient alternative to conventional stability analyses. To support our theoretical findings, we examine a four-dimensional discrete system as a special case and present numerical simulations demonstrating the effectiveness of the proposed approach. Discretization delay bifurcation control Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 29 Jul, 2025 Read the published version in Boundary Value Problems → Version 1 posted Editorial decision: Revision requested 21 Apr, 2025 Reviews received at journal 15 Apr, 2025 Reviews received at journal 01 Apr, 2025 Reviewers agreed at journal 26 Mar, 2025 Reviewers agreed at journal 26 Mar, 2025 Reviewers invited by journal 26 Mar, 2025 Editor assigned by journal 25 Mar, 2025 Submission checks completed at journal 24 Mar, 2025 First submitted to journal 22 Mar, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6283929","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":438820967,"identity":"84f36112-9c07-4dde-8f0b-05854ded20fa","order_by":0,"name":"A. M. A. 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