{"id":"https://openalex.org/W4289638026","doi":"https://doi.org/10.1155/2022/2823303","title":"Spatiotemporal Evolution Characteristics of Time\u2010Delay Ecological Competition Systems with Food\u2010Limited and Diffusion","display_name":"Spatiotemporal Evolution Characteristics of Time\u2010Delay Ecological Competition Systems with Food\u2010Limited and Diffusion","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4289638026","doi":"https://doi.org/10.1155/2022/2823303"},"language":"en","primary_location":{"id":"doi:10.1155/2022/2823303","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/2823303","pdf_url":"https://downloads.hindawi.com/journals/complexity/2022/2823303.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/2022/2823303.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073560835","display_name":"Feilong Wang","orcid":"https://orcid.org/0000-0002-2874-3936"},"institutions":[{"id":"https://openalex.org/I41198531","display_name":"Nanjing University of Posts and Telecommunications","ror":"https://ror.org/043bpky34","country_code":"CN","type":"education","lineage":["https://openalex.org/I41198531"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Feilong Wang","raw_affiliation_strings":["College of Automation & College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing 210023, China","College of Automation & College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing 210023"],"raw_orcid":"https://orcid.org/0000-0002-2874-3936","affiliations":[{"raw_affiliation_string":"College of Automation & College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing 210023, China","institution_ids":["https://openalex.org/I41198531"]},{"raw_affiliation_string":"College of Automation & College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing 210023","institution_ids":["https://openalex.org/I41198531"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054421000","display_name":"Min Xiao","orcid":"https://orcid.org/0000-0002-8992-153X"},"institutions":[{"id":"https://openalex.org/I41198531","display_name":"Nanjing University of Posts and Telecommunications","ror":"https://ror.org/043bpky34","country_code":"CN","type":"education","lineage":["https://openalex.org/I41198531"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Min Xiao","raw_affiliation_strings":["College of Automation & College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing 210023, China","College of Automation & College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing 210023"],"raw_orcid":"https://orcid.org/0000-0002-8992-153X","affiliations":[{"raw_affiliation_string":"College of Automation & College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing 210023, China","institution_ids":["https://openalex.org/I41198531"]},{"raw_affiliation_string":"College of Automation & College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing 210023","institution_ids":["https://openalex.org/I41198531"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048119294","display_name":"Zhengxin Wang","orcid":"https://orcid.org/0000-0003-2147-2229"},"institutions":[{"id":"https://openalex.org/I41198531","display_name":"Nanjing University of Posts and Telecommunications","ror":"https://ror.org/043bpky34","country_code":"CN","type":"education","lineage":["https://openalex.org/I41198531"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhengxin Wang","raw_affiliation_strings":["School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China","School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023"],"raw_orcid":"https://orcid.org/0000-0003-2147-2229","affiliations":[{"raw_affiliation_string":"School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China","institution_ids":["https://openalex.org/I41198531"]},{"raw_affiliation_string":"School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023","institution_ids":["https://openalex.org/I41198531"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063676568","display_name":"Jing Zhao","orcid":"https://orcid.org/0000-0001-9635-6551"},"institutions":[{"id":"https://openalex.org/I41198531","display_name":"Nanjing University of Posts and Telecommunications","ror":"https://ror.org/043bpky34","country_code":"CN","type":"education","lineage":["https://openalex.org/I41198531"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jing Zhao","raw_affiliation_strings":["College of Automation & College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing 210023, China","College of Automation & College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing 210023"],"raw_orcid":"https://orcid.org/0000-0001-9635-6551","affiliations":[{"raw_affiliation_string":"College of Automation & College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing 210023, China","institution_ids":["https://openalex.org/I41198531"]},{"raw_affiliation_string":"College of Automation & College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing 210023","institution_ids":["https://openalex.org/I41198531"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090305158","display_name":"Gong Chen","orcid":"https://orcid.org/0000-0002-2156-891X"},"institutions":[{"id":"https://openalex.org/I41198531","display_name":"Nanjing University of Posts and Telecommunications","ror":"https://ror.org/043bpky34","country_code":"CN","type":"education","lineage":["https://openalex.org/I41198531"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Gong Chen","raw_affiliation_strings":["College of Automation & College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing 210023, China","College of Automation & College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing 210023"],"raw_orcid":"https://orcid.org/0000-0002-2156-891X","affiliations":[{"raw_affiliation_string":"College of Automation & College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing 210023, China","institution_ids":["https://openalex.org/I41198531"]},{"raw_affiliation_string":"College of Automation & College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing 210023","institution_ids":["https://openalex.org/I41198531"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017808266","display_name":"Jinde Cao","orcid":"https://orcid.org/0000-0003-3133-7119"},"institutions":[{"id":"https://openalex.org/I193775966","display_name":"Yonsei University","ror":"https://ror.org/01wjejq96","country_code":"KR","type":"education","lineage":["https://openalex.org/I193775966"]},{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN","KR"],"is_corresponding":false,"raw_author_name":"Jinde Cao","raw_affiliation_strings":["School of Mathematics, Southeast University, Nanjing 210096, China, and Yonsei Frontier Lab,","Yonsei University, Seoul 03722, Republic of Korea","School of Mathematics, Southeast University, Nanjing 210096, China, and Yonsei Frontier Lab, Yonsei University, Seoul 03722"],"raw_orcid":"https://orcid.org/0000-0003-3133-7119","affiliations":[{"raw_affiliation_string":"School of Mathematics, Southeast University, Nanjing 210096, China, and Yonsei Frontier Lab,","institution_ids":["https://openalex.org/I76569877"]},{"raw_affiliation_string":"Yonsei University, Seoul 03722, Republic of Korea","institution_ids":["https://openalex.org/I193775966"]},{"raw_affiliation_string":"School of Mathematics, Southeast University, Nanjing 210096, China, and Yonsei Frontier Lab, Yonsei University, Seoul 03722","institution_ids":["https://openalex.org/I76569877"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5054421000"],"corresponding_institution_ids":["https://openalex.org/I41198531"],"apc_list":{"value":2550,"currency":"USD","value_usd":2550},"apc_paid":{"value":2550,"currency":"USD","value_usd":2550},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13152344,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2022","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":0.9998000264167786,"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":0.9998000264167786,"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":0.9868999719619751,"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/T11252","display_name":"Evolutionary Game Theory and Cooperation","score":0.9735999703407288,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/center-manifold","display_name":"Center manifold","score":0.7742404937744141},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6291375160217285},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.6056947112083435},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5868202447891235},{"id":"https://openalex.org/keywords/neumann-boundary-condition","display_name":"Neumann boundary condition","score":0.5806509256362915},{"id":"https://openalex.org/keywords/instability","display_name":"Instability","score":0.5059120059013367},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4857690632343292},{"id":"https://openalex.org/keywords/competition-model","display_name":"Competition model","score":0.47083401679992676},{"id":"https://openalex.org/keywords/competition","display_name":"Competition (biology)","score":0.46759432554244995},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45012569427490234},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.4298427700996399},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4034557640552521},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.40211763978004456},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.3528652787208557},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2145179808139801},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1263197362422943},{"id":"https://openalex.org/keywords/ecology","display_name":"Ecology","score":0.10990899801254272},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.10053369402885437},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.0858965516090393},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.08223924040794373}],"concepts":[{"id":"https://openalex.org/C74774103","wikidata":"https://www.wikidata.org/wiki/Q4504202","display_name":"Center manifold","level":5,"score":0.7742404937744141},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6291375160217285},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.6056947112083435},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5868202447891235},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.5806509256362915},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.5059120059013367},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4857690632343292},{"id":"https://openalex.org/C2777963317","wikidata":"https://www.wikidata.org/wiki/Q5156331","display_name":"Competition model","level":3,"score":0.47083401679992676},{"id":"https://openalex.org/C91306197","wikidata":"https://www.wikidata.org/wiki/Q45767","display_name":"Competition (biology)","level":2,"score":0.46759432554244995},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45012569427490234},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.4298427700996399},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4034557640552521},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.40211763978004456},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.3528652787208557},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2145179808139801},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1263197362422943},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.10990899801254272},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.10053369402885437},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0858965516090393},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.08223924040794373},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C181622380","wikidata":"https://www.wikidata.org/wiki/Q26911","display_name":"Profit (economics)","level":2,"score":0.0},{"id":"https://openalex.org/C175444787","wikidata":"https://www.wikidata.org/wiki/Q39072","display_name":"Microeconomics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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:10.1155/2022/2823303","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/2823303","pdf_url":"https://downloads.hindawi.com/journals/complexity/2022/2823303.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:2823303","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/complexity/2022/2823303.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:81f169130be343818279cd5c1dab5290","is_oa":true,"landing_page_url":"https://doaj.org/article/81f169130be343818279cd5c1dab5290","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":"Complexity, Vol 2022 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2022/2823303","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/2823303","pdf_url":"https://downloads.hindawi.com/journals/complexity/2022/2823303.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":0.6299999952316284,"display_name":"Zero hunger","id":"https://metadata.un.org/sdg/2"}],"awards":[{"id":"https://openalex.org/G1095396022","display_name":null,"funder_award_id":"61573194","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1810446312","display_name":null,"funder_award_id":"62073172","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2720738851","display_name":null,"funder_award_id":"ICT2022B43","funder_id":"https://openalex.org/F4320322927","funder_display_name":"Zhejiang University"},{"id":"https://openalex.org/G8820975571","display_name":null,"funder_award_id":"ICT2022B43","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"},{"id":"https://openalex.org/F4320321605","display_name":"Government of Jiangsu Province","ror":"https://ror.org/004svx814"},{"id":"https://openalex.org/F4320322927","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884"},{"id":"https://openalex.org/F4320326952","display_name":"State Key Laboratory of Industrial Control Technology","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4289638026.pdf","grobid_xml":"https://content.openalex.org/works/W4289638026.grobid-xml"},"referenced_works_count":38,"referenced_works":["https://openalex.org/W1985072454","https://openalex.org/W1985342263","https://openalex.org/W1990320498","https://openalex.org/W2013029192","https://openalex.org/W2015956660","https://openalex.org/W2019481580","https://openalex.org/W2041091952","https://openalex.org/W2054968331","https://openalex.org/W2062532291","https://openalex.org/W2066704838","https://openalex.org/W2070439973","https://openalex.org/W2461016516","https://openalex.org/W2523121418","https://openalex.org/W2524554675","https://openalex.org/W2779404005","https://openalex.org/W2889208097","https://openalex.org/W2924836965","https://openalex.org/W2931287850","https://openalex.org/W2944499181","https://openalex.org/W2990727825","https://openalex.org/W3003964932","https://openalex.org/W3016404921","https://openalex.org/W3016981486","https://openalex.org/W3021070709","https://openalex.org/W3023336365","https://openalex.org/W3029922973","https://openalex.org/W3039199027","https://openalex.org/W3047416176","https://openalex.org/W3081318027","https://openalex.org/W3108241527","https://openalex.org/W3110408755","https://openalex.org/W3142622330","https://openalex.org/W3165705034","https://openalex.org/W3166198723","https://openalex.org/W3166866323","https://openalex.org/W3175434041","https://openalex.org/W3177514385","https://openalex.org/W3189076520"],"related_works":["https://openalex.org/W1987790493","https://openalex.org/W2153388945","https://openalex.org/W1975783007","https://openalex.org/W2038701038","https://openalex.org/W2382752082","https://openalex.org/W1988489950","https://openalex.org/W4312255936","https://openalex.org/W1986426368","https://openalex.org/W2363522146","https://openalex.org/W2061491569"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"put":[4],"forward":[5],"a":[6],"time\u2010delay":[7],"ecological":[8],"competition":[9],"system":[10],"with":[11,40],"food":[12],"restriction":[13],"and":[14,32,66,86],"diffusion":[15],"terms":[16],"under":[17],"Neumann":[18],"boundary":[19],"conditions.":[20],"For":[21,37],"the":[22,26,38,42,51,55,62,67,82,87],"case":[23,39],"without":[24],"delay,":[25,41],"conditions":[27],"for":[28],"local":[29],"asymptotic":[30],"stability":[31,88],"Turing":[33],"instability":[34],"are":[35,78,97],"constructed.":[36],"existence":[43],"of":[44,54,71,84,89],"Hopf":[45],"bifurcation":[46],"is":[47],"demonstrated":[48],"by":[49,60],"analyzing":[50],"root":[52],"distribution":[53],"corresponding":[56],"characteristic":[57],"equations.":[58],"Furthermore,":[59],"using":[61],"normal":[63],"form":[64],"theory":[65],"center":[68],"manifold":[69],"reduction":[70],"partial":[72],"functional":[73],"differential":[74],"equations,":[75],"explicit":[76],"formulas":[77],"obtained":[79],"to":[80,99],"determine":[81],"direction":[83],"bifurcations":[85],"bifurcating":[90],"periodic":[91],"solutions.":[92],"Finally,":[93],"some":[94],"simulation":[95],"examples":[96],"provided":[98],"substantiate":[100],"our":[101],"analysis.":[102]},"counts_by_year":[],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
