{"id":"https://openalex.org/W1977978550","doi":"https://doi.org/10.1142/s0219525904000238","title":"PERMANENCE AND THE EXISTENCE OF THE PERIODIC SOLUTION OF THE NON-AUTONOMOUS TWO-SPECIES COMPETITIVE MODEL WITH STAGE STRUCTURE","display_name":"PERMANENCE AND THE EXISTENCE OF THE PERIODIC SOLUTION OF THE NON-AUTONOMOUS TWO-SPECIES COMPETITIVE MODEL WITH STAGE STRUCTURE","publication_year":2004,"publication_date":"2004-09-01","ids":{"openalex":"https://openalex.org/W1977978550","doi":"https://doi.org/10.1142/s0219525904000238","mag":"1977978550"},"language":"en","primary_location":{"id":"doi:10.1142/s0219525904000238","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219525904000238","pdf_url":null,"source":{"id":"https://openalex.org/S107361000","display_name":"Advances in Complex Systems","issn_l":"0219-5259","issn":["0219-5259","1793-6802","1793-9615","1793-9623"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Complex Systems","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":null,"display_name":"GUANGZHAO ZENG","orcid":null},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]},{"id":"https://openalex.org/I3130751423","display_name":"Shaoguan University","ror":"https://ror.org/0286g6711","country_code":"CN","type":"education","lineage":["https://openalex.org/I3130751423"]},{"id":"https://openalex.org/I4210092944","display_name":"Dalian University","ror":"https://ror.org/00g2ypp58","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210092944"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"GUANGZHAO ZENG","raw_affiliation_strings":["Department of Applied Mathematics,  Dalian University of Technology, DaLian, LiaoNing, 116024, P. R. China","Department of Mathematics, Shaoguan University,  ShaoGuan, GuangDong, 512005, P. R. China","Department of Applied Mathematics, Dalian University of Technology, DaLian, LiaoNing, 116024, P. R. China","Department of Mathematics, Shaoguan University, ShaoGuan, GuangDong, 512005, P. R. China"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics,  Dalian University of Technology, DaLian, LiaoNing, 116024, P. R. China","institution_ids":["https://openalex.org/I4210092944","https://openalex.org/I27357992"]},{"raw_affiliation_string":"Department of Mathematics, Shaoguan University,  ShaoGuan, GuangDong, 512005, P. R. China","institution_ids":["https://openalex.org/I3130751423"]},{"raw_affiliation_string":"Department of Applied Mathematics, Dalian University of Technology, DaLian, LiaoNing, 116024, P. R. China","institution_ids":["https://openalex.org/I27357992"]},{"raw_affiliation_string":"Department of Mathematics, Shaoguan University, ShaoGuan, GuangDong, 512005, P. R. China","institution_ids":["https://openalex.org/I3130751423"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102936938","display_name":"Lansun Chen","orcid":"https://orcid.org/0000-0003-3651-9181"},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]},{"id":"https://openalex.org/I4210092944","display_name":"Dalian University","ror":"https://ror.org/00g2ypp58","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210092944"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"LANSUN CHEN","raw_affiliation_strings":["Department of Applied Mathematics,  Dalian University of Technology, DaLian, LiaoNing, 116024, P. R. China","Department of Applied Mathematics, Dalian University of Technology, Dalian, Liaoning 116024, P. R. China"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics,  Dalian University of Technology, DaLian, LiaoNing, 116024, P. R. China","institution_ids":["https://openalex.org/I4210092944","https://openalex.org/I27357992"]},{"raw_affiliation_string":"Department of Applied Mathematics, Dalian University of Technology, Dalian, Liaoning 116024, P. R. China","institution_ids":["https://openalex.org/I27357992"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100944810","display_name":"Lihua Sun","orcid":null},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]},{"id":"https://openalex.org/I4210092944","display_name":"Dalian University","ror":"https://ror.org/00g2ypp58","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210092944"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"LIHUA SUN","raw_affiliation_strings":["Department of Applied Mathematics,  Dalian University of Technology, DaLian, LiaoNing, 116024, P. R. China","Department of Applied Mathematics, Dalian University of Technology, Dalian, Liaoning 116024, P. R. China"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics,  Dalian University of Technology, DaLian, LiaoNing, 116024, P. R. China","institution_ids":["https://openalex.org/I4210092944","https://openalex.org/I27357992"]},{"raw_affiliation_string":"Department of Applied Mathematics, Dalian University of Technology, Dalian, Liaoning 116024, P. R. China","institution_ids":["https://openalex.org/I27357992"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100761760","display_name":"Ying Liu","orcid":"https://orcid.org/0000-0002-1403-7803"},"institutions":[{"id":"https://openalex.org/I3130751423","display_name":"Shaoguan University","ror":"https://ror.org/0286g6711","country_code":"CN","type":"education","lineage":["https://openalex.org/I3130751423"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"YING LIU","raw_affiliation_strings":["Department of Mathematics, Shaoguan University,  ShaoGuan, GuangDong, 512005, P. R. China","Department of Mathematics, Shaoguan University, Shaoguan, Guangdong, 512005, P. R. China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shaoguan University,  ShaoGuan, GuangDong, 512005, P. R. China","institution_ids":["https://openalex.org/I3130751423"]},{"raw_affiliation_string":"Department of Mathematics, Shaoguan University, Shaoguan, Guangdong, 512005, P. R. China","institution_ids":["https://openalex.org/I3130751423"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I27357992","https://openalex.org/I3130751423","https://openalex.org/I4210092944"],"apc_list":null,"apc_paid":null,"fwci":0.3322,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.6863611,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"07","issue":"03n04","first_page":"385","last_page":"393"},"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":0.9958999752998352,"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":0.9958999752998352,"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/T11252","display_name":"Evolutionary Game Theory and Cooperation","score":0.9894000291824341,"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/T11031","display_name":"Game Theory and Applications","score":0.9763000011444092,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5768362283706665},{"id":"https://openalex.org/keywords/stage","display_name":"Stage (stratigraphy)","score":0.5544864535331726},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.553410530090332},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4916718602180481},{"id":"https://openalex.org/keywords/periodic-system","display_name":"Periodic system","score":0.4352056682109833},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.419039785861969},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3826509118080139},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23807120323181152},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.11106687784194946},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07833307981491089},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.0597357451915741}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5768362283706665},{"id":"https://openalex.org/C146357865","wikidata":"https://www.wikidata.org/wiki/Q1123245","display_name":"Stage (stratigraphy)","level":2,"score":0.5544864535331726},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.553410530090332},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4916718602180481},{"id":"https://openalex.org/C2989467761","wikidata":"https://www.wikidata.org/wiki/Q10693","display_name":"Periodic system","level":2,"score":0.4352056682109833},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.419039785861969},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3826509118080139},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23807120323181152},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.11106687784194946},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07833307981491089},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0597357451915741},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s0219525904000238","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219525904000238","pdf_url":null,"source":{"id":"https://openalex.org/S107361000","display_name":"Advances in Complex Systems","issn_l":"0219-5259","issn":["0219-5259","1793-6802","1793-9615","1793-9623"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Complex Systems","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:wsi:acsxxx:v:07:y:2004:i:03:p:385-393","is_oa":false,"landing_page_url":"http://www.worldscinet.com/cgi-bin/details.cgi?type=html&id=pii:S0219525904000238","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":"","raw_type":"article"},{"id":"pmh:oai:RePEc:wsi:acsxxx:v:07:y:2004:i:03n04:n:s0219525904000238","is_oa":false,"landing_page_url":"http://www.worldscientific.com/doi/abs/10.1142/S0219525904000238","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"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land","score":0.6800000071525574}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W1999341282","https://openalex.org/W2053240243","https://openalex.org/W2060796013","https://openalex.org/W2075246151"],"related_works":["https://openalex.org/W2503350049","https://openalex.org/W2329386257","https://openalex.org/W2397616145","https://openalex.org/W2397320258","https://openalex.org/W1988477118","https://openalex.org/W4324058133","https://openalex.org/W648618910","https://openalex.org/W4296658948","https://openalex.org/W3167355683","https://openalex.org/W3211565028"],"abstract_inverted_index":{"This":[0],"paper":[1],"considers":[2],"a":[3,41],"non-autonomous":[4],"competitive":[5],"two-species":[6],"model":[7,36],"with":[8],"stage":[9],"structure":[10],"in":[11],"one":[12],"species.":[13],"The":[14],"conditions":[15],"of":[16,25],"permanence":[17],"obtained.":[18],"Furthermore,":[19],"the":[20,26],"existence":[21],"and":[22],"asymptotic":[23],"stability":[24],"periodic":[27,42],"solution":[28],"are":[29],"proved":[30],"under":[31],"some":[32],"assumptions":[33],"if":[34],"this":[35],"turns":[37],"out":[38],"to":[39],"be":[40],"system.":[43]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}