Small neural networks under external forcing: Periodic pulses and Lévy noise

Small neural networks under external forcing: Periodic pulses and Lévy noise | 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 Small neural networks under external forcing: Periodic pulses and Lévy noise Elena Rybalova, Nadezhda Semenova This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4380754/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Neurons in an excitable mode do not show spiking activity and therefore do not contribute to the information transfer transmission and its processing. However, some external influences, coupling or time delay can lead to the appearance oscillations in individual systems or networks. In this study, we analyze the dynamics of a small network of locally coupled FitzHugh–Nagumo oscillators in the absence and presence of several types of external influence. Firstly, we consider the impact of periodic-pulse exposure generated as a periodic sequence of Gaussian pulses. Secondly, we show what behavior can be induced by Lévy noise and its special case, white Gaussian noise. For both types of influences, we have identified the appropriate parameters (local coupling strength, intensity, and frequency) that induces spiking activity in a small network. neural network local coupling FitzHugh–Nagumo oscillator Gaussian pulse Lévy noise Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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-4380754","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":300923645,"identity":"e0b3895f-0bd2-47f8-8433-2c57190624ce","order_by":0,"name":"Elena Rybalova","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4ElEQVRIiWNgGAWjYFACHgaGB2AG8wEgISFDnJYEMIMNREnwkKKFxwDKJQDMZ+Qe/JBQcVieXyLn86sbNRY8DOyHj27Ap0XmRl6yRMKZw4YzZ+Rus845BnQYT1raDXxaJCRyDCQS29IYN5w5u804hw2oRYLHjJAW4x9ALfb7z5x5ZpzzjzgtZkBbbBI3sPcwP85tI0YLz7s0i4QzNskzjreZMef2SfCwEfQLe+7hGx8qJGz7m5kff875VifHz374GF4tDAIJcCabBJjEqxwE+A/AmcwfCKoeBaNgFIyCEQkApSpFpQ8xWREAAAAASUVORK5CYII=","orcid":"","institution":"Saratov State University","correspondingAuthor":true,"prefix":"","firstName":"Elena","middleName":"","lastName":"Rybalova","suffix":""},{"id":300923646,"identity":"95fd00c9-6233-4c56-955a-4391e54cad00","order_by":1,"name":"Nadezhda Semenova","email":"","orcid":"","institution":"Saratov State University","correspondingAuthor":false,"prefix":"","firstName":"Nadezhda","middleName":"","lastName":"Semenova","suffix":""}],"badges":[],"createdAt":"2024-05-07 06:43:15","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-4380754/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4380754/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":57468025,"identity":"77b562a0-be75-4dfc-8d43-d1878cceb7de","added_by":"auto","created_at":"2024-05-31 05:29:20","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":10115581,"visible":true,"origin":"","legend":"","description":"","filename":"ND.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4380754/v1_covered_56e0473c-c661-4a48-8d2b-c8e6c48069e2.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Small neural networks under external forcing: Periodic pulses and Lévy noise","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"neural network, local coupling, FitzHugh–Nagumo oscillator, Gaussian pulse, Lévy noise","lastPublishedDoi":"10.21203/rs.3.rs-4380754/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4380754/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Neurons in an excitable mode do not show spiking activity and therefore do not contribute to the information transfer transmission and its processing. 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