{"id":"https://openalex.org/W4399439027","doi":"https://doi.org/10.1142/s0218127424500822","title":"Stability and Bifurcation of a Gordon\u2013Schaefer Model with Additive Allee Effect","display_name":"Stability and Bifurcation of a Gordon\u2013Schaefer Model with Additive Allee Effect","publication_year":2024,"publication_date":"2024-06-06","ids":{"openalex":"https://openalex.org/W4399439027","doi":"https://doi.org/10.1142/s0218127424500822"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127424500822","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1142/s0218127424500822","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"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":"International Journal of Bifurcation and Chaos","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/A5111223211","display_name":"Simin Liao","orcid":null},"institutions":[{"id":"https://openalex.org/I135237710","display_name":"Zhejiang Normal University","ror":"https://ror.org/01vevwk45","country_code":"CN","type":"education","lineage":["https://openalex.org/I135237710"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Simin Liao","raw_affiliation_strings":["School of Mathematics, Zhejiang Normal University, 321004 Jinhua, P. R. China"],"raw_orcid":"https://orcid.org/0009-0002-7923-9665","affiliations":[{"raw_affiliation_string":"School of Mathematics, Zhejiang Normal University, 321004 Jinhua, P. R. China","institution_ids":["https://openalex.org/I135237710"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026187828","display_name":"Yongli Song","orcid":"https://orcid.org/0000-0002-2209-2458"},"institutions":[{"id":"https://openalex.org/I163151501","display_name":"Hangzhou Normal University","ror":"https://ror.org/014v1mr15","country_code":"CN","type":"education","lineage":["https://openalex.org/I163151501"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yongli Song","raw_affiliation_strings":["School of Mathematics, Hangzhou Normal University, Hangzhou, Zhejiang 311121, P. R. China"],"raw_orcid":"https://orcid.org/0000-0002-2209-2458","affiliations":[{"raw_affiliation_string":"School of Mathematics, Hangzhou Normal University, Hangzhou, Zhejiang 311121, P. R. China","institution_ids":["https://openalex.org/I163151501"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010932652","display_name":"Yonghui Xia","orcid":"https://orcid.org/0000-0001-8918-3509"},"institutions":[{"id":"https://openalex.org/I14894300","display_name":"Foshan University","ror":"https://ror.org/02xvvvp28","country_code":"CN","type":"education","lineage":["https://openalex.org/I14894300"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yonghui Xia","raw_affiliation_strings":["School of Mathematics and Big Data, Foshan University, Foshan 528000, P. R. China"],"raw_orcid":"https://orcid.org/0000-0001-8918-3509","affiliations":[{"raw_affiliation_string":"School of Mathematics and Big Data, Foshan University, Foshan 528000, P. R. China","institution_ids":["https://openalex.org/I14894300"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4821,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.66900333,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"34","issue":"07","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":0.9979000091552734,"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":0.9979000091552734,"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":0.9937999844551086,"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/T13377","display_name":"Ecosystem dynamics and resilience","score":0.9901000261306763,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/allee-effect","display_name":"Allee effect","score":0.9970360398292542},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6064094305038452},{"id":"https://openalex.org/keywords/extinction","display_name":"Extinction (optical mineralogy)","score":0.5755225419998169},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5447190999984741},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.4779217839241028},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4724058508872986},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43453043699264526},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.39580291509628296},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3452710509300232},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19484582543373108},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14248651266098022},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.12528976798057556},{"id":"https://openalex.org/keywords/demography","display_name":"Demography","score":0.10265037417411804},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.0816250741481781}],"concepts":[{"id":"https://openalex.org/C10958125","wikidata":"https://www.wikidata.org/wiki/Q2301505","display_name":"Allee effect","level":3,"score":0.9970360398292542},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6064094305038452},{"id":"https://openalex.org/C101991246","wikidata":"https://www.wikidata.org/wiki/Q5422078","display_name":"Extinction (optical mineralogy)","level":2,"score":0.5755225419998169},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5447190999984741},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.4779217839241028},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4724058508872986},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43453043699264526},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.39580291509628296},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3452710509300232},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19484582543373108},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14248651266098022},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.12528976798057556},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.10265037417411804},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0816250741481781},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","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":1,"locations":[{"id":"doi:10.1142/s0218127424500822","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1142/s0218127424500822","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"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":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","score":0.7099999785423279,"display_name":"Life in Land"}],"awards":[{"id":"https://openalex.org/G251914666","display_name":"\u5fae\u5206\u65b9\u7a0b\u5b9a\u6027\u7406\u8bba\u4e0e\u5206\u652f\u95ee\u9898\u7814\u7a76","funder_award_id":"11931016","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5329064785","display_name":null,"funder_award_id":"LZ23A010001","funder_id":"https://openalex.org/F4320338464","funder_display_name":"Natural Science Foundation of Zhejiang Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320338464","display_name":"Natural Science Foundation of Zhejiang Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W1514578360","https://openalex.org/W1963999463","https://openalex.org/W1968748439","https://openalex.org/W1985342263","https://openalex.org/W2018897656","https://openalex.org/W2039005786","https://openalex.org/W2040653163","https://openalex.org/W2060537110","https://openalex.org/W2067962826","https://openalex.org/W2103907214","https://openalex.org/W2152029777","https://openalex.org/W2293963809","https://openalex.org/W2486760460","https://openalex.org/W2556585285","https://openalex.org/W2566360019","https://openalex.org/W2598942212","https://openalex.org/W2618890247","https://openalex.org/W2639639281","https://openalex.org/W2894384510","https://openalex.org/W2909075181","https://openalex.org/W2929444604","https://openalex.org/W2968467080","https://openalex.org/W3008800500","https://openalex.org/W3011768836","https://openalex.org/W3014961848","https://openalex.org/W3088713371","https://openalex.org/W3106935897","https://openalex.org/W3115521849","https://openalex.org/W3119169285","https://openalex.org/W3138872195","https://openalex.org/W4200610029","https://openalex.org/W4224276310","https://openalex.org/W4224444000","https://openalex.org/W4281552090","https://openalex.org/W4281929789","https://openalex.org/W4282978538","https://openalex.org/W4292994524","https://openalex.org/W4307936351","https://openalex.org/W4320018390","https://openalex.org/W4320020528","https://openalex.org/W4320020533","https://openalex.org/W4381053756","https://openalex.org/W4382984460","https://openalex.org/W4388104533"],"related_works":["https://openalex.org/W2735032095","https://openalex.org/W2107190886","https://openalex.org/W2187747741","https://openalex.org/W2774394389","https://openalex.org/W8757030","https://openalex.org/W2600193926","https://openalex.org/W2068425564","https://openalex.org/W2426442984","https://openalex.org/W4382537355","https://openalex.org/W4224217843"],"abstract_inverted_index":{"The":[0],"rarity":[1],"of":[2,13,20,51,76,90,114,135],"species":[3,15,140],"increases":[4],"its":[5,130],"market":[6],"price,":[7],"consequently":[8],"leading":[9],"to":[10,99,110,137],"the":[11,14,18,21,26,30,36,49,72,79,91,94,100,104,112,123,133,139],"overexploitation":[12],"and":[16,29,44,56,78],"even":[17],"extinction":[19],"species.":[22,115],"We":[23,68],"study":[24],"how":[25],"harvest":[27,77,106],"intensity":[28],"additive":[31,80,95],"Allee":[32,81,96,102,125],"effect":[33,82,97],"impact":[34,86],"on":[35,87],"Gordon\u2013Schaefer":[37],"model.":[38],"In":[39],"addition,":[40],"by":[41,65],"Sotomayor\u2019s":[42],"theorem":[43],"Poincar\u00e9\u2013Andronov":[45],"theorem,":[46],"we":[47,61],"prove":[48],"existence":[50],"Hopf":[52],"bifurcation,":[53,58],"saddle-node":[54],"bifurcation":[55],"transcritical":[57],"respectively.":[59],"Finally,":[60],"illustrate":[62],"our":[63],"results":[64],"numerical":[66],"simulations.":[67],"find":[69],"that":[70,121],"both":[71],"cost":[73,107],"per":[74],"unit":[75],"have":[83],"a":[84,119],"significant":[85],"human":[88],"exploitation":[89,113],"population.":[92],"As":[93],"reduces":[98],"weak":[101],"effect,":[103],"lower":[105],"encourages":[108],"humans":[109,136],"increase":[111],"This":[116],"threshold":[117],"is":[118],"switch":[120],"controls":[122],"strong":[124],"effect.":[126],"If":[127],"it":[128],"exceeds":[129],"threshold,":[131],"then":[132],"motivation":[134],"exploit":[138],"increases.":[141]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
