{"id":"https://openalex.org/W2281555966","doi":"https://doi.org/10.1142/s0218127416500061","title":"Hopf Bifurcations in Two-Strategy Delayed Replicator Dynamics","display_name":"Hopf Bifurcations in Two-Strategy Delayed Replicator Dynamics","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2281555966","doi":"https://doi.org/10.1142/s0218127416500061","mag":"2281555966"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127416500061","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416500061","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/A5004664460","display_name":"Elizabeth Wesson","orcid":"https://orcid.org/0000-0002-2536-8616"},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Elizabeth Wesson","raw_affiliation_strings":["Center for Applied Mathematics, Cornell University, Ithaca, NY 14853, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Applied Mathematics, Cornell University, Ithaca, NY 14853, USA","institution_ids":["https://openalex.org/I205783295"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078626063","display_name":"Richard H. Rand","orcid":"https://orcid.org/0000-0002-9011-2019"},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Richard Rand","raw_affiliation_strings":["Department of Mathematics, Department of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Department of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA","institution_ids":["https://openalex.org/I205783295"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101904505","display_name":"David G. Rand","orcid":"https://orcid.org/0000-0002-2821-468X"},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David Rand","raw_affiliation_strings":["Department of Psychology, Department of Economics, School of Management, Yale University, New Haven, CT 06520, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Psychology, Department of Economics, School of Management, Yale University, New Haven, CT 06520, USA","institution_ids":["https://openalex.org/I32971472"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.963,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.90807578,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"26","issue":"01","first_page":"1650006","last_page":"1650006"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11764","display_name":"Evolution and Genetic Dynamics","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11764","display_name":"Evolution and Genetic Dynamics","score":0.9998000264167786,"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":0.9993000030517578,"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9991000294685364,"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/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.7758304476737976},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.772042989730835},{"id":"https://openalex.org/keywords/replicator-equation","display_name":"Replicator equation","score":0.753606915473938},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5747945308685303},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.5293294191360474},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.5278422832489014},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.5148093104362488},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5107440948486328},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.49064841866493225},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.42187580466270447},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.41263994574546814},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36274081468582153},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.2573462128639221},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12216129899024963},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.10069477558135986}],"concepts":[{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.7758304476737976},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.772042989730835},{"id":"https://openalex.org/C50318809","wikidata":"https://www.wikidata.org/wiki/Q2145081","display_name":"Replicator equation","level":3,"score":0.753606915473938},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5747945308685303},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.5293294191360474},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5278422832489014},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.5148093104362488},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5107440948486328},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.49064841866493225},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.42187580466270447},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41263994574546814},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36274081468582153},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2573462128639221},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12216129899024963},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.10069477558135986},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127416500061","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416500061","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1964137737","https://openalex.org/W1982843671","https://openalex.org/W2028798910","https://openalex.org/W2033942534","https://openalex.org/W2077856214","https://openalex.org/W2085728653","https://openalex.org/W2125904738","https://openalex.org/W4242285942","https://openalex.org/W4249800037","https://openalex.org/W4375906334"],"related_works":["https://openalex.org/W2115351049","https://openalex.org/W2353430195","https://openalex.org/W178781247","https://openalex.org/W2094768441","https://openalex.org/W2045360568","https://openalex.org/W4206634936","https://openalex.org/W2001119836","https://openalex.org/W2522146511","https://openalex.org/W2393998944","https://openalex.org/W1964823182"],"abstract_inverted_index":{"We":[0,30,53],"investigate":[1],"the":[2,10,19,35,40,46,55,63,74,88],"dynamics":[3],"of":[4,12,18,76,87],"two-strategy":[5],"replicator":[6],"equations":[7],"in":[8,34,39,45,80],"which":[9],"fitness":[11,41],"each":[13],"strategy":[14],"is":[15],"a":[16,24,59,69],"function":[17],"population":[20],"frequencies":[21],"delayed":[22],"by":[23],"time":[25],"interval":[26],"[Formula:":[27,65],"see":[28,66],"text].":[29],"analyze":[31],"two":[32,56],"models:":[33],"first,":[36],"all":[37],"terms":[38,50],"are":[42,51],"delayed,":[43],"while":[44],"second,":[47],"only":[48],"opposite-strategy":[49],"delayed.":[52],"compare":[54],"models":[57],"via":[58],"linear":[60],"homotopy.":[61],"Taking":[62],"delay":[64],"text]":[67],"as":[68],"bifurcation":[70],"parameter,":[71],"we":[72],"demonstrate":[73],"existence":[75],"(nondegenerate)":[77],"Hopf":[78],"bifurcations":[79],"both":[81],"models,":[82],"and":[83],"present":[84],"an":[85],"analysis":[86],"resulting":[89],"limit":[90],"cycles":[91],"using":[92],"Lindstedt\u2019s":[93],"method.":[94]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":6},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
