{"id":"https://openalex.org/W2886009965","doi":"https://doi.org/10.3390/sym10080315","title":"Long Time Behavior and Global Dynamics of Simplified Von Karman Plate Without Rotational Inertia Driven by White Noise","display_name":"Long Time Behavior and Global Dynamics of Simplified Von Karman Plate Without Rotational Inertia Driven by White Noise","publication_year":2018,"publication_date":"2018-08-01","ids":{"openalex":"https://openalex.org/W2886009965","doi":"https://doi.org/10.3390/sym10080315","mag":"2886009965"},"language":"en","primary_location":{"id":"doi:10.3390/sym10080315","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10080315","pdf_url":"https://www.mdpi.com/2073-8994/10/8/315/pdf","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/10/8/315/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101543965","display_name":"Huatao Chen","orcid":null},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Huatao Chen","raw_affiliation_strings":["Division of Dynamics and Control, School of Astronautics, Harbin Institute of Technology, Harbin 150001, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Dynamics and Control, School of Astronautics, Harbin Institute of Technology, Harbin 150001, China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100773236","display_name":"Dengqing Cao","orcid":"https://orcid.org/0000-0002-3332-5704"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Dengqing Cao","raw_affiliation_strings":["Division of Dynamics and Control, School of Astronautics, Harbin Institute of Technology, Harbin 150001, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Dynamics and Control, School of Astronautics, Harbin Institute of Technology, Harbin 150001, China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047572387","display_name":"Jingfei Jiang","orcid":"https://orcid.org/0000-0003-2668-3228"},"institutions":[{"id":"https://openalex.org/I119203015","display_name":"Shandong University of Technology","ror":"https://ror.org/02mr3ar13","country_code":"CN","type":"education","lineage":["https://openalex.org/I119203015"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jingfei Jiang","raw_affiliation_strings":["Division of Dynamics and Control, School of Mathematics and Statistics, Shandong University of Technology, Zibo 255000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Dynamics and Control, School of Mathematics and Statistics, Shandong University of Technology, Zibo 255000, China","institution_ids":["https://openalex.org/I119203015"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101732505","display_name":"Xiaoming Fan","orcid":"https://orcid.org/0000-0001-6160-0286"},"institutions":[{"id":"https://openalex.org/I4800084","display_name":"Southwest Jiaotong University","ror":"https://ror.org/00hn7w693","country_code":"CN","type":"education","lineage":["https://openalex.org/I4800084"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoming Fan","raw_affiliation_strings":["School of Mathematics, Southwest Jiaotong University, Chengdu 610031, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Southwest Jiaotong University, Chengdu 610031, China","institution_ids":["https://openalex.org/I4800084"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100773236","https://openalex.org/A5101543965"],"corresponding_institution_ids":["https://openalex.org/I204983213"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.1464,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.49071798,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"10","issue":"8","first_page":"315","last_page":"315"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12206","display_name":"Vibration and Dynamic Analysis","score":0.9925000071525574,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.8262512683868408},{"id":"https://openalex.org/keywords/white-noise","display_name":"White noise","score":0.666676938533783},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5106979012489319},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4929027557373047},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47639599442481995},{"id":"https://openalex.org/keywords/inertia","display_name":"Inertia","score":0.46675848960876465},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.45459818840026855},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4462941586971283},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.41691648960113525},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3576582372188568},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.3264397978782654},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.14500415325164795},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.0752178430557251}],"concepts":[{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.8262512683868408},{"id":"https://openalex.org/C112633086","wikidata":"https://www.wikidata.org/wiki/Q381287","display_name":"White noise","level":2,"score":0.666676938533783},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5106979012489319},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4929027557373047},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47639599442481995},{"id":"https://openalex.org/C110407247","wikidata":"https://www.wikidata.org/wiki/Q122508","display_name":"Inertia","level":2,"score":0.46675848960876465},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.45459818840026855},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4462941586971283},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.41691648960113525},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3576582372188568},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3264397978782654},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.14500415325164795},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0752178430557251},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym10080315","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10080315","pdf_url":"https://www.mdpi.com/2073-8994/10/8/315/pdf","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:447483beb89a4cc79bcb5705fff5b5f9","is_oa":true,"landing_page_url":"https://doaj.org/article/447483beb89a4cc79bcb5705fff5b5f9","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 10, Iss 8, p 315 (2018)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/10/8/315/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym10080315","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym10080315","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10080315","pdf_url":"https://www.mdpi.com/2073-8994/10/8/315/pdf","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1042265011","display_name":null,"funder_award_id":"91216106","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4281043483","display_name":"\u5927\u578b\u67d4\u6027\u822a\u5929\u5668\u59ff\u6001\u8fd0\u52a8\u4e0e\u7ed3\u6784\u632f\u52a8\u7684\u8026\u5408\u52a8\u529b\u5b66\u7279\u6027\u7814\u7a76","funder_award_id":"11732005","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4817265262","display_name":null,"funder_award_id":"91216106, 11472089","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6183468723","display_name":null,"funder_award_id":"No. 11732005","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8692974840","display_name":"\u5927\u5c55\u5f26\u6bd4\u590d\u5408\u6750\u6599\u673a\u7ffc\u975e\u7ebf\u6027\u6c14\u52a8\u5f39\u6027\u7279\u5f81\u4e0e\u98a4\u632f\u7814\u7a76","funder_award_id":"11472089","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G928448623","display_name":null,"funder_award_id":"11732005;91216106;11472089","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2886009965.pdf","grobid_xml":"https://content.openalex.org/works/W2886009965.grobid-xml"},"referenced_works_count":63,"referenced_works":["https://openalex.org/W47241887","https://openalex.org/W95367681","https://openalex.org/W159942085","https://openalex.org/W1503157090","https://openalex.org/W1555942143","https://openalex.org/W1594759473","https://openalex.org/W1964264865","https://openalex.org/W1973219195","https://openalex.org/W1979597783","https://openalex.org/W1984846183","https://openalex.org/W1991729125","https://openalex.org/W1992569647","https://openalex.org/W1993739684","https://openalex.org/W1996035198","https://openalex.org/W2004610934","https://openalex.org/W2016014652","https://openalex.org/W2018243005","https://openalex.org/W2021603093","https://openalex.org/W2023743841","https://openalex.org/W2026775078","https://openalex.org/W2028226986","https://openalex.org/W2034145226","https://openalex.org/W2045411066","https://openalex.org/W2050536489","https://openalex.org/W2050652598","https://openalex.org/W2051266746","https://openalex.org/W2055236006","https://openalex.org/W2061391122","https://openalex.org/W2070430318","https://openalex.org/W2079343431","https://openalex.org/W2080625744","https://openalex.org/W2088096471","https://openalex.org/W2090667848","https://openalex.org/W2091478988","https://openalex.org/W2102621916","https://openalex.org/W2108453173","https://openalex.org/W2125366739","https://openalex.org/W2129246785","https://openalex.org/W2158122533","https://openalex.org/W2161960517","https://openalex.org/W2171419201","https://openalex.org/W2179267229","https://openalex.org/W2256678028","https://openalex.org/W2502169019","https://openalex.org/W2508497695","https://openalex.org/W2520923051","https://openalex.org/W2557804794","https://openalex.org/W2739975288","https://openalex.org/W2765707418","https://openalex.org/W2782213409","https://openalex.org/W2789918165","https://openalex.org/W2799945879","https://openalex.org/W2801038579","https://openalex.org/W2963251970","https://openalex.org/W3101143483","https://openalex.org/W4231021340","https://openalex.org/W4237082593","https://openalex.org/W4245984912","https://openalex.org/W4250087930","https://openalex.org/W4252686125","https://openalex.org/W4292366057","https://openalex.org/W4298569615","https://openalex.org/W6630012633"],"related_works":["https://openalex.org/W3049714198","https://openalex.org/W2960434112","https://openalex.org/W2036805113","https://openalex.org/W2592279130","https://openalex.org/W2049158118","https://openalex.org/W2123827981","https://openalex.org/W4205994410","https://openalex.org/W1499880030","https://openalex.org/W34461864","https://openalex.org/W4312032520"],"abstract_inverted_index":{"Without":[0],"the":[1,4,12,15,41,45,49,57,67,73,76,79,84,92,97,108,112,119,123,129,132,148,152,159],"assumption":[2],"that":[3,70,126,170],"coefficient":[5],"of":[6,14,40,56,66,75,81,83,111,122,131,147,154],"weak":[7],"damping":[8],"is":[9,181],"large":[10],"enough,":[11],"existence":[13],"global":[16,85,100,109,134,137,167],"random":[17,86,101,104,171],"attractors":[18,87],"for":[19],"simplified":[20],"Von":[21],"Karman":[22],"plate":[23,77],"without":[24],"rotational":[25],"inertia":[26],"driven":[27],"by":[28],"either":[29],"additive":[30],"white":[31,35,155],"noise":[32,36,156],"or":[33],"multiplicative":[34],"are":[37,114],"proved.":[38],"Instead":[39],"classical":[42],"splitting":[43],"method,":[44],"techniques":[46],"to":[47,158,175],"verify":[48],"asymptotic":[50],"compactness":[51],"rely":[52],"on":[53,72,96,128,166],"stabilization":[54],"estimation":[55],"system.":[58,149],"Furthermore,":[59],"a":[60,177,183],"clear":[61],"relationship":[62,98],"between":[63,99],"in-plane":[64,120],"components":[65,121],"external":[68,124],"force":[69,125],"act":[71,127],"edge":[74,130],"and":[78,103,139],"expectation":[80],"radius":[82],"can":[88],"be":[89,176],"obtained":[90],"from":[91],"theoretical":[93],"results.":[94],"Based":[95],"attractor":[102],"probability":[105],"invariant":[106],"measure,":[107],"dynamics":[110,168,179],"plates":[113],"analyzed":[115],"numerically.":[116],"With":[117],"increasing":[118,151],"plate,":[133],"D-bifurcation,":[135],"secondary":[136],"D-bifurcation":[138],"complex":[140,178],"local":[141],"dynamical":[142,160,185],"behavior":[143,161],"occur":[144],"in":[145],"motion":[146],"Moreover,":[150],"intensity":[153],"leads":[157],"becoming":[162],"simple.":[163],"The":[164],"results":[165],"reveal":[169],"snap-through":[172],"which":[173],"seems":[174],"intuitively":[180],"essentially":[182],"simple":[184],"behavior.":[186]},"counts_by_year":[{"year":2019,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}