{"id":"https://openalex.org/W4415372978","doi":"https://doi.org/10.1007/s00332-025-10211-1","title":"Existence, Upper Semicontinuity and Convergence Rate of Measure Attractors for Non-autonomous Superlinear Stochastic Schr\u00f6dinger Delay Lattice Systems","display_name":"Existence, Upper Semicontinuity and Convergence Rate of Measure Attractors for Non-autonomous Superlinear Stochastic Schr\u00f6dinger Delay Lattice Systems","publication_year":2025,"publication_date":"2025-10-21","ids":{"openalex":"https://openalex.org/W4415372978","doi":"https://doi.org/10.1007/s00332-025-10211-1"},"language":"en","primary_location":{"id":"doi:10.1007/s00332-025-10211-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00332-025-10211-1","pdf_url":null,"source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100452409","display_name":"Zhang Chen","orcid":"https://orcid.org/0000-0002-6072-8226"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhang Chen","raw_affiliation_strings":["School of Mathematics, Shandong University, Jinan, 250100, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Shandong University, Jinan, 250100, China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100369576","display_name":"Bixiang Wang","orcid":"https://orcid.org/0000-0001-5851-2453"},"institutions":[{"id":"https://openalex.org/I207123951","display_name":"New Mexico Institute of Mining and Technology","ror":"https://ror.org/005p9kw61","country_code":"US","type":"education","lineage":["https://openalex.org/I207123951"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bixiang Wang","raw_affiliation_strings":["Department of Mathematics, New Mexico Institute of Mining and Technology, Socorro, NM, 87801, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, New Mexico Institute of Mining and Technology, Socorro, NM, 87801, USA","institution_ids":["https://openalex.org/I207123951"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011911926","display_name":"Shitao Zhong","orcid":"https://orcid.org/0000-0003-3568-3924"},"institutions":[{"id":"https://openalex.org/I4210097715","display_name":"Qilu Normal University","ror":"https://ror.org/00wztsq19","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210097715"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Shitao Zhong","raw_affiliation_strings":["School of Mathematics, Qilu Normal University, Jinan, 250200, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Qilu Normal University, Jinan, 250200, China","institution_ids":["https://openalex.org/I4210097715"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5011911926","https://openalex.org/A5100452409"],"corresponding_institution_ids":["https://openalex.org/I154099455","https://openalex.org/I4210097715"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":4.0201,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.94274311,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"35","issue":"6","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11575","display_name":"Nonlinear Photonic Systems","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11575","display_name":"Nonlinear Photonic Systems","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.996399998664856,"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/pullback-attractor","display_name":"Pullback attractor","score":0.6545000076293945},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.6496000289916992},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.6384000182151794},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.6338000297546387},{"id":"https://openalex.org/keywords/probability-measure","display_name":"Probability measure","score":0.6211000084877014},{"id":"https://openalex.org/keywords/pullback","display_name":"Pullback","score":0.5573999881744385},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5004000067710876},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.4943999946117401},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.48669999837875366},{"id":"https://openalex.org/keywords/random-dynamical-system","display_name":"Random dynamical system","score":0.4839000105857849}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8184000253677368},{"id":"https://openalex.org/C2778100799","wikidata":"https://www.wikidata.org/wiki/Q7259416","display_name":"Pullback attractor","level":3,"score":0.6545000076293945},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.6496000289916992},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.6384000182151794},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.6338000297546387},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.6211000084877014},{"id":"https://openalex.org/C2777680557","wikidata":"https://www.wikidata.org/wiki/Q7259417","display_name":"Pullback","level":2,"score":0.5573999881744385},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5004000067710876},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.4943999946117401},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.48669999837875366},{"id":"https://openalex.org/C193817511","wikidata":"https://www.wikidata.org/wiki/Q7291964","display_name":"Random dynamical system","level":4,"score":0.4839000105857849},{"id":"https://openalex.org/C115667082","wikidata":"https://www.wikidata.org/wiki/Q4200518","display_name":"Invariant measure","level":3,"score":0.47040000557899475},{"id":"https://openalex.org/C75438885","wikidata":"https://www.wikidata.org/wiki/Q3403615","display_name":"Large deviations theory","level":2,"score":0.4465000033378601},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.44359999895095825},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43070000410079956},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4219000041484833},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4077000021934509},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.3871999979019165},{"id":"https://openalex.org/C2777634741","wikidata":"https://www.wikidata.org/wiki/Q768993","display_name":"Wasserstein metric","level":2,"score":0.37400001287460327},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.37290000915527344},{"id":"https://openalex.org/C2777105136","wikidata":"https://www.wikidata.org/wiki/Q827230","display_name":"Lebesgue measure","level":3,"score":0.35899999737739563},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.35740000009536743},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.34599998593330383},{"id":"https://openalex.org/C95763700","wikidata":"https://www.wikidata.org/wiki/Q578985","display_name":"Convergence of random variables","level":3,"score":0.32280001044273376},{"id":"https://openalex.org/C129301229","wikidata":"https://www.wikidata.org/wiki/Q741865","display_name":"Uniform continuity","level":3,"score":0.2883000075817108},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.28349998593330383},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.28139999508857727},{"id":"https://openalex.org/C73586568","wikidata":"https://www.wikidata.org/wiki/Q2600211","display_name":"Parameter space","level":2,"score":0.2782000005245209},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.2757999897003174},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.27309998869895935},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.2703999876976013},{"id":"https://openalex.org/C15964574","wikidata":"https://www.wikidata.org/wiki/Q7295534","display_name":"Rate function","level":3,"score":0.26910001039505005},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.2628999948501587},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.25780001282691956},{"id":"https://openalex.org/C158444337","wikidata":"https://www.wikidata.org/wiki/Q2510435","display_name":"Gibbs measure","level":2,"score":0.25450000166893005}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00332-025-10211-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00332-025-10211-1","pdf_url":null,"source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3899095673","display_name":"\u4e0d\u786e\u5b9a\u6027\u968f\u673a\u6270\u52a8\u7684\u65e0\u7a77\u7ef4\u7cfb\u7edf\u7684\u52a8\u529b\u5b66\u4e0e\u540c\u6b65\u95ee\u9898\u7814\u7a76","funder_award_id":"11971260","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":false,"pdf":false},"content_urls":null,"referenced_works_count":54,"referenced_works":["https://openalex.org/W182457466","https://openalex.org/W604134745","https://openalex.org/W1972073838","https://openalex.org/W1974439340","https://openalex.org/W1989420382","https://openalex.org/W1992384873","https://openalex.org/W2019924772","https://openalex.org/W2020897445","https://openalex.org/W2021647492","https://openalex.org/W2031489013","https://openalex.org/W2046960180","https://openalex.org/W2055655872","https://openalex.org/W2058732898","https://openalex.org/W2068597145","https://openalex.org/W2092167646","https://openalex.org/W2096112594","https://openalex.org/W2102223767","https://openalex.org/W2103893462","https://openalex.org/W2151162785","https://openalex.org/W2166757146","https://openalex.org/W2171907627","https://openalex.org/W2313187908","https://openalex.org/W2336475615","https://openalex.org/W2535231645","https://openalex.org/W2560896015","https://openalex.org/W2601210347","https://openalex.org/W2935784620","https://openalex.org/W2963078916","https://openalex.org/W2982451965","https://openalex.org/W3049192344","https://openalex.org/W3102052231","https://openalex.org/W3128738443","https://openalex.org/W3136254756","https://openalex.org/W3177105460","https://openalex.org/W3180948325","https://openalex.org/W3205838500","https://openalex.org/W3216150563","https://openalex.org/W4220932238","https://openalex.org/W4225281824","https://openalex.org/W4235356187","https://openalex.org/W4297267220","https://openalex.org/W4300475775","https://openalex.org/W4308457253","https://openalex.org/W4311083584","https://openalex.org/W4319004937","https://openalex.org/W4386101939","https://openalex.org/W4391173224","https://openalex.org/W4392374480","https://openalex.org/W4393067261","https://openalex.org/W4395000100","https://openalex.org/W4399541418","https://openalex.org/W4400226598","https://openalex.org/W4402640293","https://openalex.org/W4407635085"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":6}],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2025-10-21T00:00:00"}
