Harmonic Memory in Phasor Neural Networks

Harmonic Memory in Phasor Neural Networks | 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Download PDF Research Article Harmonic Memory in Phasor Neural Networks F. Hoppensteadt This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8788365/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 11 You are reading this latest preprint version Abstract Huygens unknowingly created a harmonic network when he mounted two pendulum clocks on a common support. The clocks were observed to synchronize—an early example of a harmonic network formed unintentionally when a designed system interacts with its substrate. Comparable substrate-mediated phenomena have been reported in biological systems. Motivated by Vinogradova’s comparator hypothesis in the limbic system, we show how a system based on canonical pendulum dynamics can realize a comparator-like mechanism in which latent harmonic structure is embedded in an interaction potential and revealed through frequency-controlled phase locking in the network of oscillators. In this framework, memories are not stored as static attractors but as oscillatory structures that are transiently expressed through resonance and phase locking. As control frequencies pass through locking regions, brief episodes of coherent high-frequency activity emerge across the system. The system developed here demonstrates how distributed oscillators can unify along a shared harmonic direction with fixed relative timing, producing system-level coherence without requiring explicit pairwise synchronization. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 16 May, 2026 Reviews received at journal 12 May, 2026 Reviewers agreed at journal 18 Mar, 2026 Reviews received at journal 10 Mar, 2026 Reviews received at journal 20 Feb, 2026 Reviewers agreed at journal 11 Feb, 2026 Reviewers agreed at journal 11 Feb, 2026 Reviewers invited by journal 08 Feb, 2026 Editor assigned by journal 08 Feb, 2026 Submission checks completed at journal 06 Feb, 2026 First submitted to journal 04 Feb, 2026 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-8788365","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":589777483,"identity":"eac20966-3868-4d5e-9395-f04664036263","order_by":0,"name":"F. 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