Particle Distribution Law Induced by Colored Noise in a Bistable Potential Field: A Counterintuitive Trimodal Distribution

Particle Distribution Law Induced by Colored Noise in a Bistable Potential Field: A Counterintuitive Trimodal Distribution | 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 Particle Distribution Law Induced by Colored Noise in a Bistable Potential Field: A Counterintuitive Trimodal Distribution Yuan-Rui Wang, Peng Wang, Qi Zhou, Guang-Kuo Zhao, Jie Huo This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7656689/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 03 Mar, 2026 Read the published version in Nonlinear Dynamics → Version 1 posted 14 You are reading this latest preprint version Abstract This paper investigates the non-equilibrium transport of particles crossing over the potential barrier in a bistable potential field driven by colored noise, and the most astonishing thing is that there exists a counter-intuitive phenomenon, the third steady state besides the normal bimodal distribution. The model, the Langevin equation , is analyzed by being transformed into the Fokker-Planck equation, and the time-dependent solution is obtained via conducting the Fourier transform. The regulatory effects of potential landscape parameter, the memory duration and intensity of the noise on the particle distribution are systematically unveiled through the calculations of the mean first passage time, diffusion coefficient, effective potential, and the spatial correlation as well. The results indicate that under a specific potential landscape, the system after a long-term evolution exhibits a trimodal distribution. The third peak is located on the right half slope of the potential barrier, which implies that colored noise induces the third steady state beyond the bistable ones. The effective potential that takes into account the contribution of colored noise reveals the influence of the noise on the particle movement/position. The spatial correlation plays a key role in enabling the particles to cross the potential barrier against the gradient force of the potential field, determining the peak position of the distribution to deviate from the bottom of the potential field, and stabilizing the third peak near the top of the potential barrier. Short-memory noise can significantly shorten the mean first passage Yuan-Rui Wang et al. time, while long-memory noise triggers a transition of the sub-diffusion to the super-diffusion. These counter-intuitive phenomena provide new insights for the control of multi-steady states and the optimization of transport in nonlinear systems. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 03 Mar, 2026 Read the published version in Nonlinear Dynamics → Version 1 posted Editorial decision: Revision requested 21 Oct, 2025 Reviews received at journal 20 Oct, 2025 Reviews received at journal 19 Oct, 2025 Reviews received at journal 14 Oct, 2025 Reviews received at journal 03 Oct, 2025 Reviewers agreed at journal 27 Sep, 2025 Reviewers agreed at journal 25 Sep, 2025 Reviewers agreed at journal 23 Sep, 2025 Reviewers agreed at journal 22 Sep, 2025 Reviewers agreed at journal 22 Sep, 2025 Reviewers invited by journal 22 Sep, 2025 Editor assigned by journal 22 Sep, 2025 Submission checks completed at journal 22 Sep, 2025 First submitted to journal 19 Sep, 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-7656689","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":521628088,"identity":"02a20d54-50c1-4e7b-8911-f1f36ecc31c5","order_by":0,"name":"Yuan-Rui Wang","email":"","orcid":"","institution":"Ningxia University","correspondingAuthor":false,"prefix":"","firstName":"Yuan-Rui","middleName":"","lastName":"Wang","suffix":""},{"id":521628089,"identity":"fc0df56f-d986-4985-918f-62f91551b1e7","order_by":1,"name":"Peng 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The model, the Langevin equation , is analyzed by being transformed into the Fokker-Planck equation, and the time-dependent solution is obtained via conducting the Fourier transform. The regulatory effects of potential landscape parameter, the memory duration and intensity of the noise on the particle distribution are systematically unveiled through the calculations of the mean first passage time, diffusion coefficient, effective potential, and the spatial correlation as well. The results indicate that under a specific potential landscape, the system after a long-term evolution exhibits a trimodal distribution. The third peak is located on the right half slope of the potential barrier, which implies that colored noise induces the third steady state beyond the bistable ones. The effective potential that takes into account the contribution of colored noise reveals the influence of the noise on the particle movement/position. 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