Hopf Bifurcation Analysis and Control of Traffic Flow Models Considering Driver Reaction Effects

Hopf Bifurcation Analysis and Control of Traffic Flow Models Considering Driver Reaction Effects | 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 Hopf Bifurcation Analysis and Control of Traffic Flow Models Considering Driver Reaction Effects WenHuan Ai, DongQiang Su, ShaoKang Wang, XiaoYi Shi, LingYi OuYang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7853070/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 10 Mar, 2026 Read the published version in Nonlinear Dynamics → Version 1 posted 13 You are reading this latest preprint version Abstract Various traffic phenomena, such as traffic congestion, stop-and-go waves, and shock waves, often occur alternately in traffic systems. The essence of these abrupt changes lies in bifurcation behaviors triggered by different causes in traffic flow. When the traffic system passes through certain critical bifurcation points, the qualitative state of the system changes suddenly, leading to traffic instability. Based on a macroscopic traffic flow model that incorporates driver reaction effects, this paper employs bifurcation theory in nonlinear dynamics to analyze traffic congestion and stability transitions caused by bifurcations in traffic systems. First, the linear stability region of the macroscopic model is derived using linear stability theory. Second, bifurcation analysis is conducted on the macroscopic model to determine the conditions for the existence of Hopf bifurcations, identify stability changes in the traffic system, and analyze the relationship between stability transitions and bifurcation points. Finally, for unstable bifurcation points, a feedback controller is designed using nonlinear feedback control methods. By regulating the amplitude of the Hopf bifurcation limit cycle, the onset of the Hopf bifurcation is delayed, thereby alleviating traffic congestion. Driver reaction effects Vehicle inertia effects Macroscopic continuous model Bifurcation analysis Hopf bifurcation control Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 10 Mar, 2026 Read the published version in Nonlinear Dynamics → Version 1 posted Editorial decision: Revision requested 01 Dec, 2025 Reviews received at journal 01 Dec, 2025 Reviews received at journal 24 Nov, 2025 Reviews received at journal 10 Nov, 2025 Reviewers agreed at journal 03 Nov, 2025 Reviews received at journal 03 Nov, 2025 Reviewers agreed at journal 03 Nov, 2025 Reviewers agreed at journal 28 Oct, 2025 Reviewers agreed at journal 28 Oct, 2025 Reviewers invited by journal 27 Oct, 2025 Editor assigned by journal 20 Oct, 2025 Submission checks completed at journal 13 Oct, 2025 First submitted to journal 13 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. 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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-7853070","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":539459518,"identity":"644e3e27-b310-44e8-b159-a4621db8aee6","order_by":0,"name":"WenHuan 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