Boundary control of random reaction-diffusion neural networks with time-varying delay

Boundary control of random reaction-diffusion neural networks with time-varying 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 Boundary control of random reaction-diffusion neural networks with time-varying delay Zhuo Xue, Kai-Ning Wu, Yongxin Wu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7934535/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 10 You are reading this latest preprint version Abstract Recently, the study of random ordinary differential systems, which are driven by second-order moment processes rather than Brownian motion, has attracted increasing attention. This paper investigates the random reaction-diffusion neural networks (RRDNNs) with time-varying delay. The boundary stabilisation of the system is investigated under reasonable assumptions. Stability criteria for ensuring asymptotic stability under the designed controller are derived and the effect of system parameters and time delay on stability is analysed. Additionally, under milder conditions, the noise-to-state stability (NSS) of the system with a boundary controller is discussed, and condition that guarantees NSS for time-delay systems is established. This work represents a pioneering effort in the study of random nonlinear systems within the domain of partial differential equations, particularly focusing on time-delay reaction-diffusion equations. Finally, numerical simulations are conducted to validate the theoretical results. Random nonlinear systems reaction-diffusion neural networks time-varying delay boundary control Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 23 Mar, 2026 Reviews received at journal 03 Dec, 2025 Reviews received at journal 02 Dec, 2025 Reviewers agreed at journal 14 Nov, 2025 Reviewers agreed at journal 13 Nov, 2025 Reviewers agreed at journal 12 Nov, 2025 Reviewers invited by journal 12 Nov, 2025 Editor assigned by journal 11 Nov, 2025 Submission checks completed at journal 31 Oct, 2025 First submitted to journal 23 Oct, 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. 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