{"id":"https://openalex.org/W2986508947","doi":"https://doi.org/10.1155/2019/4873290","title":"Dynamic Analysis of Stochastic Lotka\u2013Volterra Predator\u2010Prey Model with Discrete Delays and Feedback Control","display_name":"Dynamic Analysis of Stochastic Lotka\u2013Volterra Predator\u2010Prey Model with Discrete Delays and Feedback Control","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2986508947","doi":"https://doi.org/10.1155/2019/4873290","mag":"2986508947"},"language":"en","primary_location":{"id":"doi:10.1155/2019/4873290","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/4873290","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/4873290.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/2019/4873290.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101624059","display_name":"Jinlei Liu","orcid":"https://orcid.org/0000-0002-9811-2179"},"institutions":[{"id":"https://openalex.org/I80143920","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98","country_code":"CN","type":"education","lineage":["https://openalex.org/I80143920"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jinlei Liu","raw_affiliation_strings":["College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China","College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China","institution_ids":["https://openalex.org/I80143920"]},{"raw_affiliation_string":"College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590","institution_ids":["https://openalex.org/I80143920"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018091212","display_name":"Wencai Zhao","orcid":"https://orcid.org/0000-0003-4689-695X"},"institutions":[{"id":"https://openalex.org/I4210115539","display_name":"Ministry of Science","ror":"https://ror.org/023ktd084","country_code":"ME","type":"government","lineage":["https://openalex.org/I4210115539"]},{"id":"https://openalex.org/I80143920","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98","country_code":"CN","type":"education","lineage":["https://openalex.org/I80143920"]}],"countries":["CN","ME"],"is_corresponding":true,"raw_author_name":"Wencai Zhao","raw_affiliation_strings":["College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China","State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, China","College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590","State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China","institution_ids":["https://openalex.org/I80143920"]},{"raw_affiliation_string":"State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, China","institution_ids":["https://openalex.org/I80143920"]},{"raw_affiliation_string":"College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590","institution_ids":["https://openalex.org/I80143920"]},{"raw_affiliation_string":"State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590","institution_ids":["https://openalex.org/I80143920","https://openalex.org/I4210115539"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5018091212"],"corresponding_institution_ids":["https://openalex.org/I4210115539","https://openalex.org/I80143920"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":1.3322,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.82143091,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9995999932289124,"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"}},{"id":"https://openalex.org/T11764","display_name":"Evolution and Genetic Dynamics","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10410","display_name":"COVID-19 epidemiological studies","score":0.9585000276565552,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6669005155563354},{"id":"https://openalex.org/keywords/feedback-control","display_name":"Feedback control","score":0.6057388782501221},{"id":"https://openalex.org/keywords/predation","display_name":"Predation","score":0.5225745439529419},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4777740240097046},{"id":"https://openalex.org/keywords/volterra-equations","display_name":"Volterra equations","score":0.47640955448150635},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46833133697509766},{"id":"https://openalex.org/keywords/predator","display_name":"Predator","score":0.4557792842388153},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.4195072054862976},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.39125898480415344},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36439841985702515},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.25690826773643494},{"id":"https://openalex.org/keywords/ecology","display_name":"Ecology","score":0.16626542806625366},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.14814162254333496},{"id":"https://openalex.org/keywords/control-engineering","display_name":"Control engineering","score":0.13717734813690186},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.11667138338088989},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07795113325119019},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.07331150770187378},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06411316990852356}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6669005155563354},{"id":"https://openalex.org/C3018651601","wikidata":"https://www.wikidata.org/wiki/Q183635","display_name":"Feedback control","level":2,"score":0.6057388782501221},{"id":"https://openalex.org/C188382862","wikidata":"https://www.wikidata.org/wiki/Q170430","display_name":"Predation","level":2,"score":0.5225745439529419},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4777740240097046},{"id":"https://openalex.org/C2983756050","wikidata":"https://www.wikidata.org/wiki/Q150052","display_name":"Volterra equations","level":3,"score":0.47640955448150635},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46833133697509766},{"id":"https://openalex.org/C96857902","wikidata":"https://www.wikidata.org/wiki/Q2138108","display_name":"Predator","level":3,"score":0.4557792842388153},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.4195072054862976},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.39125898480415344},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36439841985702515},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.25690826773643494},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.16626542806625366},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.14814162254333496},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.13717734813690186},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.11667138338088989},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07795113325119019},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.07331150770187378},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06411316990852356},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2019/4873290","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/4873290","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/4873290.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:4873290","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/8503/2019/4873290.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:b221d15718c8407891096077a757e4f6","is_oa":true,"landing_page_url":"https://doaj.org/article/b221d15718c8407891096077a757e4f6","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"}],"best_oa_location":{"id":"doi:10.1155/2019/4873290","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/4873290","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/4873290.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":[],"awards":[{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5501176208","display_name":null,"funder_award_id":"11371230","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6130374233","display_name":null,"funder_award_id":"2014TDJH102)","funder_id":"https://openalex.org/F4320322522","funder_display_name":"Shandong University of Science and Technology"},{"id":"https://openalex.org/G7108638857","display_name":null,"funder_award_id":"2014TDJH102","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G879360056","display_name":null,"funder_award_id":"2014TDJH102","funder_id":"https://openalex.org/F4320322522","funder_display_name":"Shandong University of Science and Technology"},{"id":"https://openalex.org/G8963529913","display_name":null,"funder_award_id":"11371230","funder_id":"https://openalex.org/F4320322522","funder_display_name":"Shandong University of Science and Technology"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322522","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2986508947.pdf","grobid_xml":"https://content.openalex.org/works/W2986508947.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W659339155","https://openalex.org/W2011141068","https://openalex.org/W2021599539","https://openalex.org/W2044697359","https://openalex.org/W2049410683","https://openalex.org/W2049550645","https://openalex.org/W2052943368","https://openalex.org/W2058732322","https://openalex.org/W2076603886","https://openalex.org/W2562844658","https://openalex.org/W2773322315","https://openalex.org/W2773960616","https://openalex.org/W2775390262","https://openalex.org/W2775620382","https://openalex.org/W2793347221","https://openalex.org/W2802660328","https://openalex.org/W2806959187","https://openalex.org/W2886385593","https://openalex.org/W2888548938","https://openalex.org/W2889417563","https://openalex.org/W2898911081","https://openalex.org/W2906574471","https://openalex.org/W2909849241","https://openalex.org/W2916365025","https://openalex.org/W2918025530","https://openalex.org/W2919273974","https://openalex.org/W2920889573","https://openalex.org/W2921737079","https://openalex.org/W2921804423","https://openalex.org/W2932986619","https://openalex.org/W2940950468","https://openalex.org/W2942886942","https://openalex.org/W2946842329","https://openalex.org/W2949448993","https://openalex.org/W2964800720","https://openalex.org/W2975278558"],"related_works":["https://openalex.org/W2168669462","https://openalex.org/W2192426841","https://openalex.org/W2067000585","https://openalex.org/W4323811225","https://openalex.org/W2164070575","https://openalex.org/W4311356582","https://openalex.org/W2289298756","https://openalex.org/W2073795128","https://openalex.org/W2143533297","https://openalex.org/W2075391697"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"a":[3],"stochastic":[4,34],"Lotka\u2013Volterra":[5],"predator\u2010prey":[6],"model":[7,45],"with":[8],"discrete":[9],"delays":[10],"and":[11,19,46,53],"feedback":[12],"control":[13],"is":[14,65],"studied.":[15],"Firstly,":[16],"the":[17,30,37,42,51,56,59,62],"existence":[18],"uniqueness":[20],"of":[21,33,41,55,61],"global":[22],"positive":[23,38],"solution":[24],"are":[25],"proved.":[26],"Further,":[27],"we":[28],"investigate":[29],"asymptotic":[31],"property":[32],"system":[35],"at":[36],"equilibrium":[39],"point":[40],"corresponding":[43],"deterministic":[44],"establish":[47],"sufficient":[48],"conditions":[49],"for":[50],"persistence":[52],"extinction":[54],"model.":[57],"Finally,":[58],"correctness":[60],"theoretical":[63],"derivation":[64],"verified":[66],"by":[67],"numerical":[68],"simulations.":[69]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3}],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2025-10-10T00:00:00"}
