{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T21:40:29Z","timestamp":1783978829089,"version":"3.55.0"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2024,8,30]],"date-time":"2024-08-30T00:00:00Z","timestamp":1724976000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,8,30]],"date-time":"2024-08-30T00:00:00Z","timestamp":1724976000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Syst Sci Complex"],"published-print":{"date-parts":[[2024,10]]},"DOI":"10.1007\/s11424-024-2477-9","type":"journal-article","created":{"date-parts":[[2024,8,30]],"date-time":"2024-08-30T11:03:18Z","timestamp":1725015798000},"page":"1978-1994","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Flocking Effects of the Stochastic Cucker-Smale System with Noise"],"prefix":"10.1007","volume":"37","author":[{"given":"Ning","family":"Han","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bin","family":"Ge","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lin","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,8,30]]},"reference":[{"issue":"10","key":"2477_CR1","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1063\/1.2800090","volume":"60","author":"T Feder","year":"2007","unstructured":"Feder T, Statistical physics is for the birds, Physics Today, 2007, 60(10): 28\u201330.","journal-title":"Physics Today"},{"issue":"3\u20134","key":"2477_CR2","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1016\/j.physrep.2012.03.004","volume":"517","author":"T Vicsek","year":"2012","unstructured":"Vicsek T, Collective motion, Physics Reports, 2012, 517(3\u20134): 71\u2013140.","journal-title":"Physics Reports"},{"issue":"46","key":"2477_CR3","doi-asserted-by":"publisher","first-page":"18720","DOI":"10.1073\/pnas.1107583108","volume":"108","author":"Y Katz","year":"2011","unstructured":"Katz Y, Tunstrm K, Ioannoua C C, et al., Inferring the structure and dynamics of interactions in schooling fish, Proceedings of the National Academy of Sciences, 2011, 108(46): 18720\u201318725.","journal-title":"Proceedings of the National Academy of Sciences"},{"issue":"6","key":"2477_CR4","doi-asserted-by":"publisher","first-page":"1226","DOI":"10.1103\/PhysRevLett.75.1226","volume":"75","author":"T Vicsek","year":"1995","unstructured":"Vicsek T, Czir\u00f3k A, Ben-Jacob E, et al. Novel type of phase transition in a system of self-driven particles, Physical Review Letters, 1995, 75(6): 1226.","journal-title":"Physical Review Letters"},{"issue":"5","key":"2477_CR5","doi-asserted-by":"publisher","first-page":"852","DOI":"10.1109\/TAC.2007.895842","volume":"52","author":"F Cucker","year":"2007","unstructured":"Cucker F and Smale S, Emergent behavior in flocks, IEEE Transactions on Automatic Control, 2007, 52(5): 852\u2013862.","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"10","key":"2477_CR6","doi-asserted-by":"publisher","first-page":"103301","DOI":"10.1063\/1.3496895","volume":"51","author":"S M Ahn","year":"2010","unstructured":"Ahn S M and Ha S Y, Stochastic flocking dynamics of the Cucker-Smale model with multiplicative white noises, Journal of Mathematical Physics, 2010, 51(10): 103301.","journal-title":"Journal of Mathematical Physics"},{"issue":"1","key":"2477_CR7","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1016\/j.jmaa.2014.01.036","volume":"415","author":"Y Liu","year":"2014","unstructured":"Liu Y and Wu J, Flocking and asymptotic velocity of the Cucker-Smale model with processing delay, Journal of Mathematical Analysis and Applications, 2014, 415(1): 53\u201361.","journal-title":"Journal of Mathematical Analysis and Applications"},{"key":"2477_CR8","doi-asserted-by":"publisher","first-page":"1011","DOI":"10.3934\/krm.2017040","volume":"10","author":"Y P Choi","year":"2017","unstructured":"Choi Y P and Haskovec J, Cucker-Smale model with normalized communication weights and time delay, Kinetic and Related Models, 2017, 10: 1011\u20131033.","journal-title":"Kinetic and Related Models"},{"issue":"8","key":"2477_CR9","doi-asserted-by":"publisher","first-page":"2053","DOI":"10.4310\/CMS.2018.v16.n8.a1","volume":"16","author":"C Pignotti","year":"2018","unstructured":"Pignotti C and Trlat E, Convergence to consensus of the general finite-dimensional Cucker-Smale model with time-varying delays, Communications in Mathematical Sciences, 2018, 16(8): 2053\u20132076.","journal-title":"Communications in Mathematical Sciences"},{"issue":"10\u201311","key":"2477_CR10","first-page":"1002","volume":"17","author":"W Ren","year":"2010","unstructured":"Ren W and Atkins E, Distributed multi-vehicle coordinated control via local information exchange, International Journal of Robust and Nonlinear Control: IFAC-Affiliated Journal, 2010, 17(10\u201311): 1002\u20131033.","journal-title":"International Journal of Robust and Nonlinear Control: IFAC-Affiliated Journal"},{"issue":"S1","key":"2477_CR11","doi-asserted-by":"publisher","first-page":"354","DOI":"10.1002\/cplx.21747","volume":"21","author":"Y Han","year":"2016","unstructured":"Han Y, Zhao D, and Sun Y, Finite-time flocking problem of a cucker-smale-type self-propelled particle model, Complexity, 2016, 21(S1): 354\u2013361.","journal-title":"Complexity"},{"key":"2477_CR12","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1016\/j.physa.2014.05.008","volume":"410","author":"Z C Li","year":"2014","unstructured":"Li Z C and Xue X P, Cucker-Smale flocking under rooted leadership with free-will agents, Physica A: Statistical Mechanics and Its Applications, 2014, 410: 205\u2013217.","journal-title":"Physica A: Statistical Mechanics and Its Applications"},{"issue":"8","key":"2477_CR13","doi-asserted-by":"publisher","first-page":"083118","DOI":"10.1063\/1.4929496","volume":"25","author":"Y Sun","year":"2015","unstructured":"Sun Y and Lin W, A positive role of multiplicative noise on the emergence of flocking in a stochastic Cucker-Smale system, Chaos: An Interdisciplinary Journal of Nonlinear Science, 2015, 25(8): 083118.","journal-title":"Chaos: An Interdisciplinary Journal of Nonlinear Science"},{"issue":"2","key":"2477_CR14","doi-asserted-by":"publisher","first-page":"453","DOI":"10.4310\/CMS.2009.v7.n2.a9","volume":"7","author":"S Y Ha","year":"2009","unstructured":"Ha S Y, Lee K, and Levy D, Emergence of time-asymptotic flocking in a stochastic Cucker-Smale system, Communications in Mathematical Sciences, 2009, 7(2): 453\u2013469.","journal-title":"Communications in Mathematical Sciences"},{"issue":"9","key":"2477_CR15","doi-asserted-by":"publisher","first-page":"1653","DOI":"10.1142\/S0218202520500335","volume":"30","author":"S Y Ha","year":"2020","unstructured":"Ha S Y, Li Z, and Zhang X T, On the critical exponent of the one-dimensional Cucker-Smale model on a general graph, Mathematical Models and Methods in Applied Sciences, 2020, 30(9): 1653\u20131703.","journal-title":"Mathematical Models and Methods in Applied Sciences"},{"issue":"2","key":"2477_CR16","doi-asserted-by":"publisher","first-page":"625","DOI":"10.4310\/CMS.2012.v10.n2.a10","volume":"10","author":"S Ahn","year":"2012","unstructured":"Ahn S, Choi H, Ha S Y, et al., On the collision avoiding initial-congurations to the Cucker-Smale type flocking models, Communications in Mathematical Sciences, 2012, 10(2): 625\u2013643.","journal-title":"Communications in Mathematical Sciences"},{"key":"2477_CR17","first-page":"317","volume":"37","author":"J A Carrillo","year":"2017","unstructured":"Carrillo J A, Choi Y P, Mucha P B, et al., Sharp conditions to avoid collisions in singular Cucker-Smale interactions, Nonlinear Analysis: Real World Applications, 2017, 37: 317\u2013328.","journal-title":"Nonlinear Analysis: Real World Applications"},{"issue":"5","key":"2477_CR18","doi-asserted-by":"publisher","first-page":"1238","DOI":"10.1109\/TAC.2010.2042355","volume":"55","author":"F Cucker","year":"2010","unstructured":"Cucker F and Dong J G, Avoiding collisions in flocks, IEEE Transactions on Automatic Control, 2010, 55(5): 1238\u20131243.","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"4","key":"2477_CR19","doi-asserted-by":"publisher","first-page":"689","DOI":"10.1090\/S0033-569X-2014-01350-5","volume":"72","author":"S Y Ha","year":"2014","unstructured":"Ha S Y, Li Z C, Slemrod M, et al., Flocking behavior of the Cucker-Smale model under rooted leadership in a large coupling limit, Quarterly of Applied Mathematics, 2014, 72(4): 689\u2013701.","journal-title":"Quarterly of Applied Mathematics"},{"issue":"3","key":"2477_CR20","doi-asserted-by":"publisher","first-page":"694","DOI":"10.1137\/060673254","volume":"68","author":"J Shen","year":"2007","unstructured":"Shen J, Cucker-Smale flocking under hierarchical leadership, SIAM Journal on Applied Mathematics, 2007, 68(3): 694\u2013719.","journal-title":"SIAM Journal on Applied Mathematics"},{"issue":"4","key":"2477_CR21","doi-asserted-by":"publisher","first-page":"693","DOI":"10.1090\/qam\/1401","volume":"73","author":"Z C Li","year":"2015","unstructured":"Li Z C and Ha S Y, On the Cucker-Smale flocking with alternating leaders, Quarterly of Applied Mathematics, 2015, 73(4): 693\u2013709.","journal-title":"Quarterly of Applied Mathematics"},{"issue":"8","key":"2477_CR22","doi-asserted-by":"publisher","first-page":"3156","DOI":"10.1137\/100791774","volume":"70","author":"Z C Li","year":"2010","unstructured":"Li Z C and Xue X P, Cucker-Smale flocking under rooted leadership with fixed and switching topologies, SIAM Journal on Applied Mathematics, 2010, 70(8): 3156\u20133174.","journal-title":"SIAM Journal on Applied Mathematics"},{"issue":"4","key":"2477_CR23","doi-asserted-by":"publisher","first-page":"1307","DOI":"10.1137\/100785910","volume":"71","author":"F Dalmao","year":"2011","unstructured":"Dalmao F and Mordecki E, Cucker-Smale flocking under hierarchical leadership and random interactions, SIAM Journal on Applied Mathematics, 2011, 71(4): 1307\u20131316.","journal-title":"SIAM Journal on Applied Mathematics"},{"issue":"15","key":"2477_CR24","doi-asserted-by":"publisher","first-page":"2066","DOI":"10.1016\/j.fss.2010.03.006","volume":"161","author":"D Lin","year":"2010","unstructured":"Lin D and Wang X, Observer-based decentralized fuzzy neural sliding mode control for interconnected unknown chaotic systems via network structure adaptation, Fuzzy Sets and Systems, 2010, 161(15): 2066\u20132080.","journal-title":"Fuzzy Sets and Systems"},{"issue":"4","key":"2477_CR25","doi-asserted-by":"publisher","first-page":"435","DOI":"10.1016\/j.physleta.2007.07.053","volume":"372","author":"X Y Wang","year":"2008","unstructured":"Wang X Y and He Y J, Projective synchronization of fractional order chaotic system based on linear separation, Physics Letters A, 2008, 372(4): 435\u2013441.","journal-title":"Physics Letters A"},{"issue":"8","key":"2477_CR26","doi-asserted-by":"publisher","first-page":"3351","DOI":"10.1016\/j.cnsns.2009.01.010","volume":"14","author":"X Y Wang","year":"2009","unstructured":"Wang X Y and Song J M, Synchronization of the fractional order hyberchaos Lorenz systems with activation feedback control, Communications in Nonlinear Science and Numerical Simulation, 2009, 14(8): 3351\u20133357.","journal-title":"Communications in Nonlinear Science and Numerical Simulation"},{"issue":"3","key":"2477_CR27","doi-asserted-by":"publisher","first-page":"033106","DOI":"10.1063\/1.2755420","volume":"17","author":"X Y Wang","year":"2007","unstructured":"Wang X Y and Wang M J, Dynamic analysis of the fractional-order Liu system and its system and its synchronization, Chaos: An Interdisciplinary Journal of Nonlinear Science, 2007, 17(3): 033106.","journal-title":"Chaos: An Interdisciplinary Journal of Nonlinear Science"},{"issue":"11","key":"2477_CR28","doi-asserted-by":"publisher","first-page":"5511","DOI":"10.1109\/TAC.2017.2691303","volume":"62","author":"X Yang","year":"2017","unstructured":"Yang X, Lam J, Ho D W C, et al., Fixed-time synchronization of complex networks with impulsive effects via non-chattering control, IEEE Transactions on Automatic Control, 2017, 62(11): 5511\u20135521.","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"6","key":"2477_CR29","doi-asserted-by":"publisher","first-page":"1498","DOI":"10.1007\/s11424-019-7407-x","volume":"32","author":"G Chen","year":"2019","unstructured":"Chen G and Liu Z, Flocking with general local interaction and large population, Journal of Systems Science and Complexity, 2019, 32(6): 1498\u20131525.","journal-title":"Journal of Systems Science and Complexity"},{"issue":"1","key":"2477_CR30","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1007\/s11424-021-0026-3","volume":"35","author":"Z Qiao","year":"2022","unstructured":"Qiao Z, Liu Y, and Wang X, Multi-cluster flocking behavior analysis for a delayed Cucker-Smale model with short-range communication weight, Journal of Systems Science and Complexity, 2022, 35(1): 137\u2013158.","journal-title":"Journal of Systems Science and Complexity"},{"key":"2477_CR31","volume-title":"Spectral Graph Theory","author":"F R K Chung","year":"1997","unstructured":"Chung F R K, Spectral Graph Theory, American Mathematical Society, Rhode Island, 1997."},{"issue":"9","key":"2477_CR32","first-page":"15","volume":"61","author":"R P Agaev","year":"2000","unstructured":"Agaev R P and Chebotarev P Y, The matrix of maximal outgoing forests of digraph and its applications, Institute of Control Sciences, 2000, 61(9): 15\u201343.","journal-title":"Institute of Control Sciences"},{"issue":"4","key":"2477_CR33","doi-asserted-by":"publisher","first-page":"950","DOI":"10.1109\/TAC.2010.2041610","volume":"55","author":"L Wang","year":"2010","unstructured":"Wang L and Xiao F, Finite-time consensus problems for networks of dynamic agents, IEEE Transactions on Automatic Control, 2010, 55(4): 950\u2013955.","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"8","key":"2477_CR34","doi-asserted-by":"publisher","first-page":"2106","DOI":"10.1109\/TAC.2011.2179869","volume":"57","author":"A Polyakov","year":"2011","unstructured":"Polyakov A, Nonlinear feedback design for fixed-time stabilization of linear control systems, IEEE Transactions on Automatic Control, 2011, 57(8): 2106\u20132110.","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"12","key":"2477_CR35","doi-asserted-by":"publisher","first-page":"2105","DOI":"10.1016\/j.automatica.2010.08.009","volume":"46","author":"W Chen","year":"2010","unstructured":"Chen W and Jiao L C, Finite-time stability theorem of stochastic nonlinear systems, Automatica, 2010, 46(12): 2105\u20132108.","journal-title":"Automatica"},{"key":"2477_CR36","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1016\/j.neucom.2014.11.044","volume":"153","author":"D Xie","year":"2015","unstructured":"Xie D and Liang T, Second-order group consensus for multi-agent systems with time delays, Neurocomputing, 2015, 153: 133\u2013139.","journal-title":"Neurocomputing"},{"key":"2477_CR37","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139020411","volume-title":"Matrix Analysis","author":"R A Horn","year":"2012","unstructured":"Horn R A and Johnson C R, Matrix Analysis, Cambridge University Press, Cambridge, 2012."}],"container-title":["Journal of Systems Science and Complexity"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11424-024-2477-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11424-024-2477-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11424-024-2477-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,30]],"date-time":"2024-08-30T11:21:30Z","timestamp":1725016890000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11424-024-2477-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,30]]},"references-count":37,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2024,10]]}},"alternative-id":["2477"],"URL":"https:\/\/doi.org\/10.1007\/s11424-024-2477-9","relation":{},"ISSN":["1009-6124","1559-7067"],"issn-type":[{"value":"1009-6124","type":"print"},{"value":"1559-7067","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,8,30]]},"assertion":[{"value":"1 December 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 August 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 August 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no conflict of interest.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of Interest"}}]}}