{"id":"https://openalex.org/W2032316550","doi":"https://doi.org/10.1137/120878537","title":"Hopf Bifurcations and Limit Cycles in Evolutionary Network Dynamics","display_name":"Hopf Bifurcations and Limit Cycles in Evolutionary Network Dynamics","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2032316550","doi":"https://doi.org/10.1137/120878537","mag":"2032316550"},"language":"en","primary_location":{"id":"doi:10.1137/120878537","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120878537","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical 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":"https://openalex.org/A5068512038","display_name":"Darren Pais","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Darren Pais","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111420770","display_name":"Carlos H. Caicedo-N\u00fa\u00f1ez","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Carlos H. Caicedo-N\u00fan\u0342ez","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5032304399","display_name":"Naomi Ehrich Leonard","orcid":"https://orcid.org/0000-0002-5328-3871"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Naomi E. Leonard","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5068512038"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":13.5851,"has_fulltext":false,"cited_by_count":58,"citation_normalized_percentile":{"value":0.98372083,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"11","issue":"4","first_page":"1754","last_page":"1784"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11252","display_name":"Evolutionary Game Theory and Cooperation","score":0.996399998664856,"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"}},"topics":[{"id":"https://openalex.org/T11252","display_name":"Evolutionary Game Theory and Cooperation","score":0.996399998664856,"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/T11764","display_name":"Evolution and Genetic Dynamics","score":0.9958999752998352,"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/T11031","display_name":"Game Theory and Applications","score":0.9815000295639038,"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/limit","display_name":"Limit (mathematics)","score":0.6427850723266602},{"id":"https://openalex.org/keywords/evolutionary-dynamics","display_name":"Evolutionary dynamics","score":0.6249978542327881},{"id":"https://openalex.org/keywords/replicator-equation","display_name":"Replicator equation","score":0.6031926870346069},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.5770282745361328},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.565345823764801},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.5595866441726685},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4800528287887573},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4256145656108856},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3914172947406769},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.36678045988082886},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.21933409571647644},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1805787980556488},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17009618878364563},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13447770476341248}],"concepts":[{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6427850723266602},{"id":"https://openalex.org/C171578705","wikidata":"https://www.wikidata.org/wiki/Q5418700","display_name":"Evolutionary dynamics","level":3,"score":0.6249978542327881},{"id":"https://openalex.org/C50318809","wikidata":"https://www.wikidata.org/wiki/Q2145081","display_name":"Replicator equation","level":3,"score":0.6031926870346069},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.5770282745361328},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.565345823764801},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.5595866441726685},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4800528287887573},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4256145656108856},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3914172947406769},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.36678045988082886},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.21933409571647644},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1805787980556488},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17009618878364563},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13447770476341248},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"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},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/120878537","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120878537","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.387.1764","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.387.1764","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.princeton.edu/~naomi/publications/2012/PaisSIADS12.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.6200000047683716}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1512042876","https://openalex.org/W1534391781","https://openalex.org/W1596321532","https://openalex.org/W1960351623","https://openalex.org/W1983982862","https://openalex.org/W1986380555","https://openalex.org/W2006656562","https://openalex.org/W2009389773","https://openalex.org/W2011849203","https://openalex.org/W2026796238","https://openalex.org/W2027610319","https://openalex.org/W2028798910","https://openalex.org/W2029530361","https://openalex.org/W2036083037","https://openalex.org/W2039446744","https://openalex.org/W2047647995","https://openalex.org/W2051290456","https://openalex.org/W2082519494","https://openalex.org/W2083568566","https://openalex.org/W2085156013","https://openalex.org/W2089876099","https://openalex.org/W2096500735","https://openalex.org/W2097141283","https://openalex.org/W2111250529","https://openalex.org/W2117359342","https://openalex.org/W2131579317","https://openalex.org/W2132304982","https://openalex.org/W2155470302","https://openalex.org/W2157639208","https://openalex.org/W2610857016","https://openalex.org/W3171836044","https://openalex.org/W4211095127"],"related_works":["https://openalex.org/W2115351049","https://openalex.org/W2353430195","https://openalex.org/W2094768441","https://openalex.org/W178781247","https://openalex.org/W2901407768","https://openalex.org/W2054345477","https://openalex.org/W2045360568","https://openalex.org/W2001119836","https://openalex.org/W2522146511","https://openalex.org/W2922337407"],"abstract_inverted_index":{"The":[0,116],"replicator-mutator":[1,59],"equations":[2,60],"from":[3,78],"evolutionary":[4],"dynamics":[5,16,22,34,85,105],"serve":[6],"as":[7],"a":[8,37],"model":[9],"for":[10,70,137],"the":[11,29,40,58,71,84,87,94,104,113,140,150],"evolution":[12,127],"of":[13,28,32,73,83,89,103,122],"language,":[14],"behavioral":[15,132],"in":[17,23,39,44,53,86,112,125,131,134,147],"social":[18,135],"networks,":[19],"and":[20,55,64,128],"decision-making":[21,138],"networked":[24],"multiagent":[25],"systems.":[26],"Analysis":[27],"stable":[30,74,100],"equilibria":[31],"these":[33],"has":[35],"been":[36],"focus":[38],"literature,":[41],"where":[42],"symmetry":[43],"fitness":[45,54,91],"functions":[46],"is":[47],"typically":[48],"assumed.":[49],"We":[50,67],"explore":[51],"asymmetry":[52],"show":[56],"that":[57],"exhibit":[61],"Hopf":[62,81],"bifurcations":[63,82],"limit":[65,75,101,117,141],"cycles.":[66],"prove":[68],"conditions":[69],"existence":[72],"cycles":[76,102,111,118,142],"arising":[77],"multiple":[79],"distinct":[80],"case":[88,96],"circulant":[90],"matrices.":[92],"In":[93],"noncirculant":[95],"we":[97],"illustrate":[98],"how":[99],"are":[106],"coupled":[107],"to":[108,120,129,144],"embedded":[109],"directed":[110],"payoff":[114],"graph.":[115],"correspond":[119,143],"oscillations":[121,130,146],"grammar":[123],"dominance":[124],"language":[126],"preferences":[133],"networks;":[136],"systems,":[139],"sustained":[145],"decisions":[148],"across":[149],"group.":[151]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":4}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
