{"id":"https://openalex.org/W2909016487","doi":"https://doi.org/10.1155/2019/4681205","title":"Dynamical Analysis of a Stochastic Multispecies Turbidostat Model","display_name":"Dynamical Analysis of a Stochastic Multispecies Turbidostat Model","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2909016487","doi":"https://doi.org/10.1155/2019/4681205","mag":"2909016487"},"language":"en","primary_location":{"id":"doi:10.1155/2019/4681205","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/4681205","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/4681205.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/complexity/2019/4681205.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004399252","display_name":"Yu Mu","orcid":"https://orcid.org/0000-0003-0938-228X"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]},{"id":"https://openalex.org/I4210106563","display_name":"Hubei University for Nationalities","ror":"https://ror.org/01q349q17","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210106563"]},{"id":"https://openalex.org/I75900474","display_name":"Hubei University","ror":"https://ror.org/03a60m280","country_code":"CN","type":"education","lineage":["https://openalex.org/I75900474"]}],"countries":["CN","HK"],"is_corresponding":false,"raw_author_name":"Yu Mu","raw_affiliation_strings":["Department of Mathematics, City University of Hong Kong, Hong Kong, China","Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000, China","Department of Mathematics, City University of Hong Kong, Hong Kong","Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, City University of Hong Kong, Hong Kong, China","institution_ids":["https://openalex.org/I168719708"]},{"raw_affiliation_string":"Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000, China","institution_ids":["https://openalex.org/I75900474","https://openalex.org/I4210106563"]},{"raw_affiliation_string":"Department of Mathematics, City University of Hong Kong, Hong Kong","institution_ids":["https://openalex.org/I168719708"]},{"raw_affiliation_string":"Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000","institution_ids":["https://openalex.org/I75900474","https://openalex.org/I4210106563"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010951763","display_name":"Zuxiong Li","orcid":"https://orcid.org/0000-0002-2526-8113"},"institutions":[{"id":"https://openalex.org/I4210106563","display_name":"Hubei University for Nationalities","ror":"https://ror.org/01q349q17","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210106563"]},{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]},{"id":"https://openalex.org/I75900474","display_name":"Hubei University","ror":"https://ror.org/03a60m280","country_code":"CN","type":"education","lineage":["https://openalex.org/I75900474"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zuxiong Li","raw_affiliation_strings":["Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000, China","School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China","Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000","School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000, China","institution_ids":["https://openalex.org/I75900474","https://openalex.org/I4210106563"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China","institution_ids":["https://openalex.org/I47720641"]},{"raw_affiliation_string":"Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000","institution_ids":["https://openalex.org/I75900474","https://openalex.org/I4210106563"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030204812","display_name":"Huili Xiang","orcid":"https://orcid.org/0000-0003-3713-0813"},"institutions":[{"id":"https://openalex.org/I4210106563","display_name":"Hubei University for Nationalities","ror":"https://ror.org/01q349q17","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210106563"]},{"id":"https://openalex.org/I75900474","display_name":"Hubei University","ror":"https://ror.org/03a60m280","country_code":"CN","type":"education","lineage":["https://openalex.org/I75900474"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huili Xiang","raw_affiliation_strings":["Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000, China","Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000, China","institution_ids":["https://openalex.org/I75900474","https://openalex.org/I4210106563"]},{"raw_affiliation_string":"Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000","institution_ids":["https://openalex.org/I75900474","https://openalex.org/I4210106563"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015758523","display_name":"Hailing Wang","orcid":"https://orcid.org/0000-0003-0333-5044"},"institutions":[{"id":"https://openalex.org/I4210106563","display_name":"Hubei University for Nationalities","ror":"https://ror.org/01q349q17","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210106563"]},{"id":"https://openalex.org/I75900474","display_name":"Hubei University","ror":"https://ror.org/03a60m280","country_code":"CN","type":"education","lineage":["https://openalex.org/I75900474"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hailing Wang","raw_affiliation_strings":["Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000, China","Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000, China","institution_ids":["https://openalex.org/I75900474","https://openalex.org/I4210106563"]},{"raw_affiliation_string":"Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000","institution_ids":["https://openalex.org/I75900474","https://openalex.org/I4210106563"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5010951763"],"corresponding_institution_ids":["https://openalex.org/I4210106563","https://openalex.org/I47720641","https://openalex.org/I75900474"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":1.597,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.87610252,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"2019","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11252","display_name":"Evolutionary Game Theory and Cooperation","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/3312","display_name":"Sociology and Political Science"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11252","display_name":"Evolutionary Game Theory and Cooperation","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/3312","display_name":"Sociology and Political Science"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T13377","display_name":"Ecosystem dynamics and resilience","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2306","display_name":"Global and Planetary Change"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/competition","display_name":"Competition (biology)","score":0.5687811970710754},{"id":"https://openalex.org/keywords/white-noise","display_name":"White noise","score":0.5650402307510376},{"id":"https://openalex.org/keywords/stochastic-modelling","display_name":"Stochastic modelling","score":0.5631041526794434},{"id":"https://openalex.org/keywords/dilution","display_name":"Dilution","score":0.46302762627601624},{"id":"https://openalex.org/keywords/biological-system","display_name":"Biological system","score":0.45547887682914734},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.45012804865837097},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.439301460981369},{"id":"https://openalex.org/keywords/competitive-exclusion","display_name":"Competitive exclusion","score":0.43793830275535583},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38904571533203125},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3631851077079773},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3254152536392212},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.325208842754364},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.23984748125076294},{"id":"https://openalex.org/keywords/ecology","display_name":"Ecology","score":0.20172876119613647},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.11994606256484985},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.11159828305244446},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11044564843177795},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08171302080154419},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.0804310142993927}],"concepts":[{"id":"https://openalex.org/C91306197","wikidata":"https://www.wikidata.org/wiki/Q45767","display_name":"Competition (biology)","level":2,"score":0.5687811970710754},{"id":"https://openalex.org/C112633086","wikidata":"https://www.wikidata.org/wiki/Q381287","display_name":"White noise","level":2,"score":0.5650402307510376},{"id":"https://openalex.org/C127491075","wikidata":"https://www.wikidata.org/wiki/Q7617825","display_name":"Stochastic modelling","level":2,"score":0.5631041526794434},{"id":"https://openalex.org/C96618451","wikidata":"https://www.wikidata.org/wiki/Q3028008","display_name":"Dilution","level":2,"score":0.46302762627601624},{"id":"https://openalex.org/C186060115","wikidata":"https://www.wikidata.org/wiki/Q30336093","display_name":"Biological system","level":1,"score":0.45547887682914734},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.45012804865837097},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.439301460981369},{"id":"https://openalex.org/C2992687717","wikidata":"https://www.wikidata.org/wiki/Q1331830","display_name":"Competitive exclusion","level":3,"score":0.43793830275535583},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38904571533203125},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3631851077079773},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3254152536392212},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.325208842754364},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.23984748125076294},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.20172876119613647},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.11994606256484985},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.11159828305244446},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11044564843177795},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08171302080154419},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0804310142993927}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2019/4681205","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/4681205","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/4681205.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:complx:4681205","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/8503/2019/4681205.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:e4a8732dfe8f42f293b3fc816af400e6","is_oa":true,"landing_page_url":"https://doaj.org/article/e4a8732dfe8f42f293b3fc816af400e6","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Complexity, Vol 2019 (2019)","raw_type":"article"},{"id":"pmh:oai:pure.atira.dk:publications/9d50c30e-d8bf-49d0-bd30-e0fdb0d7f158","is_oa":true,"landing_page_url":"https://hdl.handle.net/2031/9d50c30e-d8bf-49d0-bd30-e0fdb0d7f158","pdf_url":null,"source":{"id":"https://openalex.org/S7407055387","display_name":"CityU Scholars","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mu, Y, Li, Z, Xiang, H & Wang, H 2019, 'Dynamical Analysis of a Stochastic Multispecies Turbidostat Model', Complexity, vol. 2019, 4681205. https://doi.org/10.1155/2019/4681205","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2019/4681205","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/4681205","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/4681205.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.8199999928474426,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G6749455390","display_name":null,"funder_award_id":"11561022","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7595537803","display_name":null,"funder_award_id":"11701163","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7931910575","display_name":null,"funder_award_id":"2014M562008","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"},{"id":"https://openalex.org/F4320323298","display_name":"H\u00e1sk\u00f3li \u00cdslands","ror":"https://ror.org/01db6h964"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2909016487.pdf","grobid_xml":"https://content.openalex.org/works/W2909016487.grobid-xml"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W246955972","https://openalex.org/W1494628843","https://openalex.org/W1590937957","https://openalex.org/W1750885354","https://openalex.org/W1966202707","https://openalex.org/W1983659903","https://openalex.org/W1988681504","https://openalex.org/W1989998020","https://openalex.org/W1994609212","https://openalex.org/W1996153408","https://openalex.org/W2008850057","https://openalex.org/W2026995646","https://openalex.org/W2032820131","https://openalex.org/W2053410410","https://openalex.org/W2057425267","https://openalex.org/W2062247832","https://openalex.org/W2077392233","https://openalex.org/W2088792404","https://openalex.org/W2121397953","https://openalex.org/W2165842301","https://openalex.org/W2200387372","https://openalex.org/W2201340799","https://openalex.org/W2223090614","https://openalex.org/W2252189398","https://openalex.org/W2283052995","https://openalex.org/W2321342852","https://openalex.org/W2326010876","https://openalex.org/W2415858019","https://openalex.org/W2506243456","https://openalex.org/W2511722628","https://openalex.org/W2517452708","https://openalex.org/W2564445370","https://openalex.org/W2652668669","https://openalex.org/W2773322315","https://openalex.org/W2775259738","https://openalex.org/W2796542623","https://openalex.org/W2796676362","https://openalex.org/W2796941167","https://openalex.org/W2963624172","https://openalex.org/W3021557197","https://openalex.org/W3022581161","https://openalex.org/W4237564398","https://openalex.org/W4297440205"],"related_works":["https://openalex.org/W2042280983","https://openalex.org/W1989733110","https://openalex.org/W2321888438","https://openalex.org/W2888652631","https://openalex.org/W1995427843","https://openalex.org/W3119323248","https://openalex.org/W2369445029","https://openalex.org/W2026456043","https://openalex.org/W1987284827","https://openalex.org/W4320063126"],"abstract_inverted_index":{"A":[0],"stochastic":[1,37,49],"turbidostat":[2],"system":[3],"in":[4,16,63],"which":[5],"the":[6,25,34,40,44,53,59],"dilution":[7],"rate":[8],"is":[9,14],"subject":[10],"to":[11],"white":[12],"noise":[13],"investigated":[15],"this":[17,64],"paper.":[18],"First":[19],"of":[20,24,36,56],"all,":[21],"sufficient":[22],"conditions":[23],"competitive":[26],"exclusion":[27],"among":[28,46],"microorganisms":[29,47],"are":[30,66],"obtained":[31,62],"by":[32,68],"employing":[33],"techniques":[35],"analysis.":[38],"Furthermore,":[39],"results":[41,61],"demonstrate":[42],"that":[43],"competition":[45],"and":[48],"disturbance":[50],"will":[51],"affect":[52],"dynamical":[54],"behaviors":[55],"microorganisms.":[57],"Finally,":[58],"theoretical":[60],"contribution":[65],"illustrated":[67],"numerical":[69],"simulations.":[70]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}