{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,31]],"date-time":"2026-05-31T11:00:32Z","timestamp":1780225232843,"version":"3.54.0"},"reference-count":35,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12371243"],"award-info":[{"award-number":["12371243"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Communications in Nonlinear Science and Numerical Simulation"],"published-print":{"date-parts":[[2026,10]]},"DOI":"10.1016\/j.cnsns.2026.110055","type":"journal-article","created":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T19:57:24Z","timestamp":1776283044000},"page":"110055","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"P1","title":["Stochastic Cucker-Smale model with interaction potential and common noise: Well-posedness, mean-field limit and flocking"],"prefix":"10.1016","volume":"161","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0833-9119","authenticated-orcid":false,"given":"Jizhao","family":"Huang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yan","family":"Lv","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wei","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.cnsns.2026.110055_bib0001","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1109\/JPROC.2006.887295","article-title":"Collective motion, sensor networks, and ocean sampling","volume":"95","author":"Leonard","year":"2007","journal-title":"Proc IEEE"},{"key":"10.1016\/j.cnsns.2026.110055_bib0002","doi-asserted-by":"crossref","first-page":"4828","DOI":"10.1103\/PhysRevE.58.4828","article-title":"Flocks, herds, and schools: a quantitative theory of flocking","volume":"58","author":"Toner","year":"1998","journal-title":"Phys Rev E"},{"issue":"5","key":"10.1016\/j.cnsns.2026.110055_bib0003","doi-asserted-by":"crossref","first-page":"852","DOI":"10.1109\/TAC.2007.895842","article-title":"Emergent behavior in flocks","volume":"52","author":"Cucker","year":"2007","journal-title":"IEEE Trans Automat Control"},{"issue":"3","key":"10.1016\/j.cnsns.2026.110055_bib0004","doi-asserted-by":"crossref","first-page":"2554","DOI":"10.1016\/j.jde.2016.11.017","article-title":"Emergent dynamics of cucker-smale flocking particles in a random environment","volume":"262","author":"Ha","year":"2017","journal-title":"J Differ Equ"},{"issue":"25","key":"10.1016\/j.cnsns.2026.110055_bib0005","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.jde.2021.02.046","article-title":"Collective stochastic dynamics of the cucker-smale ensemble under uncertain communication","volume":"284","author":"Ha","year":"2021","journal-title":"J Differ Equ"},{"issue":"1","key":"10.1016\/j.cnsns.2026.110055_bib0006","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1017\/apr.2025.10024","article-title":"Well-posedness and averaging principle for non-gaussian McKean-Vlasov stochastic differential equations with locally Lipschitz coefficients","volume":"58","author":"Chao","year":"2026","journal-title":"Adv Appl Probab"},{"key":"10.1016\/j.cnsns.2026.110055_bib0007","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1016\/j.spa.2022.04.012","article-title":"Well-posedness and propagation of chaos for McKean-Vlasov equations with jumps and locally Lipschitz coefficients","volume":"150","author":"Erny","year":"2022","journal-title":"Stochastic Process Appl"},{"issue":"2","key":"10.1016\/j.cnsns.2026.110055_bib0008","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1007\/s11118-023-10113-5","article-title":"Distribution-path dependent nonlinear SPDEs with application to stochastic transport type equations","volume":"61","author":"Ren","year":"2024","journal-title":"Potential Anal"},{"key":"10.1016\/j.cnsns.2026.110055_bib0009","unstructured":"Hong W., Li S.H., Liu W., Mckean-Vlasov stochastic partial differential equations: existence, uniqueness and propagation of chaos. 2023. arXiv: 2306.15508."},{"issue":"2","key":"10.1016\/j.cnsns.2026.110055_bib0010","doi-asserted-by":"crossref","first-page":"2136","DOI":"10.1214\/23-AAP2016","article-title":"Mckean-Vlasov sde and SPDE with locally monotone coefficients","volume":"34","author":"Hong","year":"2024","journal-title":"Ann Appl Probab"},{"issue":"3","key":"10.1016\/j.cnsns.2026.110055_bib0011","doi-asserted-by":"crossref","first-page":"573","DOI":"10.3934\/krm.2019023","article-title":"Cucker-Smale flocking particles with multiplicative noises: stochastic mean-field limit and phase transition","volume":"12","author":"Choi","year":"2019","journal-title":"Kinet Relat Models"},{"issue":"2","key":"10.1016\/j.cnsns.2026.110055_bib0012","doi-asserted-by":"crossref","first-page":"1115","DOI":"10.1137\/20M1324454","article-title":"Multiflocks: emergent dynamics in systems with multiscale collective behavior","volume":"19","author":"Shvydkoy","year":"2021","journal-title":"Multiscale Model Sim"},{"issue":"15","key":"10.1016\/j.cnsns.2026.110055_bib0013","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1016\/j.jde.2023.08.027","article-title":"Pattern formation in the Cucker-Smale model","volume":"376","author":"Zhang","year":"2023","journal-title":"J Differ Equ"},{"issue":"4","key":"10.1016\/j.cnsns.2026.110055_bib0014","doi-asserted-by":"crossref","first-page":"1535","DOI":"10.1137\/15M1030467","article-title":"A Cucker-Smale model with noise and delay","volume":"76","author":"Erban","year":"2016","journal-title":"SIAM J Appl Math"},{"key":"10.1016\/j.cnsns.2026.110055_bib0015","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/j.aml.2018.06.018","article-title":"Emergent behavior of Cucker-Smale flocking particles with heterogeneous time delays","volume":"86","author":"Choi","year":"2018","journal-title":"Appl Math Lett"},{"issue":"5","key":"10.1016\/j.cnsns.2026.110055_bib0016","doi-asserted-by":"crossref","first-page":"3239","DOI":"10.1214\/18-AAP1400","article-title":"Stochastic Cucker-Smale models: old and new","volume":"28","author":"Cattiaux","year":"2018","journal-title":"Ann Appl Probab"},{"key":"10.1016\/j.cnsns.2026.110055_bib0017","doi-asserted-by":"crossref","DOI":"10.1063\/1.3496895","article-title":"Stochastic flocking dynamics of the Cucker-Smale model with multiplicative white noises","volume":"51","author":"Ahn","year":"2010","journal-title":"J Math Phys"},{"issue":"5","key":"10.1016\/j.cnsns.2026.110055_bib0018","doi-asserted-by":"crossref","first-page":"4219","DOI":"10.1007\/s12190-024-02128-x","article-title":"Strong stochastic flocking with noise under long-range fat tail communication","volume":"70","author":"Zhao","year":"2024","journal-title":"J Appl Math Comput"},{"issue":"4","key":"10.1016\/j.cnsns.2026.110055_bib0019","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1007\/s00033-024-02291-y","article-title":"A strong form of propagation of chaos for Cucker-Smale model","volume":"75","author":"Wu","year":"2024","journal-title":"Z Angew Math Phys"},{"issue":"11","key":"10.1016\/j.cnsns.2026.110055_bib0020","doi-asserted-by":"crossref","first-page":"2179","DOI":"10.1142\/S0218202511005702","article-title":"Stochastic mean-field limit: non-Lipschitz forces and swarming","volume":"21","author":"Bolley","year":"2011","journal-title":"Math Mod Meth Appl S"},{"issue":"1","key":"10.1016\/j.cnsns.2026.110055_bib0021","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1007\/s00332-020-09661-6","article-title":"The microscopic derivation and well-posedness of the stochastic Keller-Segel equation","volume":"31","author":"Huang","year":"2021","journal-title":"J Nonlinear Sci"},{"key":"10.1016\/j.cnsns.2026.110055_bib0022","doi-asserted-by":"crossref","first-page":"428","DOI":"10.1016\/j.jde.2021.04.002","article-title":"One dimensional singular Cucker-Smale model: uniform-in-time mean-field limit and contractivity","volume":"287","author":"Choi","year":"2021","journal-title":"J Differ Equ"},{"issue":"7","key":"10.1016\/j.cnsns.2026.110055_bib0023","doi-asserted-by":"crossref","first-page":"2186","DOI":"10.3934\/cpaa.2023063","article-title":"The stochastic flocking model with far-field degenerate communication","volume":"22","author":"Lv","year":"2023","journal-title":"Commun Pure Appl Anal"},{"issue":"6","key":"10.1016\/j.cnsns.2026.110055_bib0024","doi-asserted-by":"crossref","first-page":"895","DOI":"10.3934\/krm.2022017","article-title":"Propagation of chaos: a review of models, methods and applications. I. models and methods","volume":"15","author":"Chaintron","year":"2022","journal-title":"Kinet Relat Models"},{"key":"10.1016\/j.cnsns.2026.110055_bib0025","series-title":"Optimal Transport: Old and New","author":"Villani","year":"2008"},{"key":"10.1016\/j.cnsns.2026.110055_bib0026","series-title":"Markov Processes: Characterization and Convergence","author":"Ethier","year":"1986"},{"key":"10.1016\/j.cnsns.2026.110055_bib0027","doi-asserted-by":"crossref","first-page":"1667","DOI":"10.3934\/dcds.2020336","article-title":"Mckean-Vlasov sdes with drifts discontinuous under wasserstein distance","volume":"41","author":"Huang","year":"2021","journal-title":"Discrete Contin Dyn Syst"},{"key":"10.1016\/j.cnsns.2026.110055_bib0028","series-title":"Probabilistic Theory of Mean Field Games with Applications I-II","author":"Carmona","year":"2018"},{"key":"10.1016\/j.cnsns.2026.110055_bib0029","doi-asserted-by":"crossref","unstructured":"Liu Z., Ma J., Existence, uniqueness and ergodicity for Mckean-Vlasov sdes under distribution-dependent Lyapunov conditions. 2023. arXiv: 2309.05411.","DOI":"10.2139\/ssrn.4641739"},{"key":"10.1016\/j.cnsns.2026.110055_bib0030","series-title":"Stochastic Differential Equations and Applications","author":"Mao","year":"2007"},{"key":"10.1016\/j.cnsns.2026.110055_bib0031","doi-asserted-by":"crossref","DOI":"10.1016\/j.physd.2023.133739","article-title":"The large-time behavior of the vlasov alignment model with power-law or riesz potentials","volume":"448","author":"Chen","year":"2023","journal-title":"Physica D"},{"issue":"2","key":"10.1016\/j.cnsns.2026.110055_bib0032","doi-asserted-by":"crossref","first-page":"753","DOI":"10.1214\/22-AIHP1337","article-title":"Global contractivity for langevin dynamics with distribution-dependent forces and uniform in time propagation of chaos","volume":"60","author":"Schuh","year":"2024","journal-title":"Ann Inst H Poincar\u00e9 Probab Statist"},{"key":"10.1016\/j.cnsns.2026.110055_bib0033","doi-asserted-by":"crossref","DOI":"10.1016\/j.cnsns.2022.106474","article-title":"Controlled pattern formation of stochastic Cucker-Smale systems with network structures","volume":"111","author":"Choi","year":"2022","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"10.1016\/j.cnsns.2026.110055_bib0034","doi-asserted-by":"crossref","unstructured":"Tadmor E., On the mathematics of swarming: Emergent behavior in alignment dynamics. 2021. arXiv: 2102.09134.","DOI":"10.1090\/noti2254"},{"issue":"06","key":"10.1016\/j.cnsns.2026.110055_bib0035","doi-asserted-by":"crossref","first-page":"1191","DOI":"10.1142\/S0218202516500287","article-title":"Emergence of bi-cluster flocking for the Cucker-Smale model","volume":"26","author":"Cho","year":"2016","journal-title":"Math Mod Meth Appl S"}],"container-title":["Communications in Nonlinear Science and Numerical Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1007570426004144?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1007570426004144?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,5,31]],"date-time":"2026-05-31T10:03:01Z","timestamp":1780221781000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S1007570426004144"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10]]},"references-count":35,"alternative-id":["S1007570426004144"],"URL":"https:\/\/doi.org\/10.1016\/j.cnsns.2026.110055","relation":{},"ISSN":["1007-5704"],"issn-type":[{"value":"1007-5704","type":"print"}],"subject":[],"published":{"date-parts":[[2026,10]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Stochastic Cucker-Smale model with interaction potential and common noise: Well-posedness, mean-field limit and flocking","name":"articletitle","label":"Article Title"},{"value":"Communications in Nonlinear Science and Numerical Simulation","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cnsns.2026.110055","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"110055"}}