{"id":"https://openalex.org/W2138385728","doi":"https://doi.org/10.1137/130932272","title":"Codimension-Two Bifurcations in Animal Aggregation Models with Symmetry","display_name":"Codimension-Two Bifurcations in Animal Aggregation Models with Symmetry","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2138385728","doi":"https://doi.org/10.1137/130932272","mag":"2138385728"},"language":"en","primary_location":{"id":"doi:10.1137/130932272","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130932272","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":true,"oa_status":"green","oa_url":"https://discovery.dundee.ac.uk/ws/files/51734058/SymmetryCod2Aggmodels_Buono_Eftimie_SIADS_FinalVersion.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085865750","display_name":"Pietro-Luciano Buono","orcid":"https://orcid.org/0000-0003-1460-4465"},"institutions":[{"id":"https://openalex.org/I39470171","display_name":"University of Ontario Institute of Technology","ror":"https://ror.org/016zre027","country_code":"CA","type":"education","lineage":["https://openalex.org/I39470171"]},{"id":"https://openalex.org/I4210161785","display_name":"First Technical University","ror":"https://ror.org/05tb13r23","country_code":"NG","type":"education","lineage":["https://openalex.org/I4210161785"]}],"countries":["CA","NG"],"is_corresponding":true,"raw_author_name":"Pietro-Luciano Buono","raw_affiliation_strings":["Ontario Tech University"],"affiliations":[{"raw_affiliation_string":"Ontario Tech University","institution_ids":["https://openalex.org/I39470171","https://openalex.org/I4210161785"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006689072","display_name":"Raluca Eftimie","orcid":"https://orcid.org/0000-0002-9726-1498"},"institutions":[{"id":"https://openalex.org/I177639307","display_name":"University of Dundee","ror":"https://ror.org/03h2bxq36","country_code":"GB","type":"education","lineage":["https://openalex.org/I177639307"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Raluca Eftimie","raw_affiliation_strings":["University of Dundee"],"affiliations":[{"raw_affiliation_string":"University of Dundee","institution_ids":["https://openalex.org/I177639307"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5085865750"],"corresponding_institution_ids":["https://openalex.org/I39470171","https://openalex.org/I4210161785"],"apc_list":null,"apc_paid":null,"fwci":2.2509,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.88437517,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"13","issue":"4","first_page":"1542","last_page":"1582"},"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/T11252","display_name":"Evolutionary Game Theory and Cooperation","score":0.9959999918937683,"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.8297383785247803},{"id":"https://openalex.org/keywords/pattern-formation","display_name":"Pattern formation","score":0.6360162496566772},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6185540556907654},{"id":"https://openalex.org/keywords/equivariant-map","display_name":"Equivariant map","score":0.6092812418937683},{"id":"https://openalex.org/keywords/codimension","display_name":"Codimension","score":0.5863257646560669},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5380614995956421},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5275185704231262},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.508470892906189},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4778594374656677},{"id":"https://openalex.org/keywords/steady-state","display_name":"Steady state (chemistry)","score":0.4751567542552948},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4532424807548523},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.43872836232185364},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4279441237449646},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.4229205250740051},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.37842679023742676},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3394154906272888},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.24374178051948547},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19760757684707642},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08798816800117493},{"id":"https://openalex.org/keywords/ecology","display_name":"Ecology","score":0.08650603890419006}],"concepts":[{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.8297383785247803},{"id":"https://openalex.org/C207016750","wikidata":"https://www.wikidata.org/wiki/Q1955627","display_name":"Pattern formation","level":2,"score":0.6360162496566772},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6185540556907654},{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.6092812418937683},{"id":"https://openalex.org/C83979697","wikidata":"https://www.wikidata.org/wiki/Q1778247","display_name":"Codimension","level":2,"score":0.5863257646560669},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5380614995956421},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5275185704231262},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.508470892906189},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4778594374656677},{"id":"https://openalex.org/C8171440","wikidata":"https://www.wikidata.org/wiki/Q903414","display_name":"Steady state (chemistry)","level":2,"score":0.4751567542552948},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4532424807548523},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.43872836232185364},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4279441237449646},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.4229205250740051},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37842679023742676},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3394154906272888},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24374178051948547},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19760757684707642},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08798816800117493},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.08650603890419006},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C147789679","wikidata":"https://www.wikidata.org/wiki/Q11372","display_name":"Physical chemistry","level":1,"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/130932272","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130932272","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:discovery.dundee.ac.uk:openaire/58f0f4be-7c02-4c33-a44a-e90213f893f1","is_oa":true,"landing_page_url":"https://discovery.dundee.ac.uk/en/publications/58f0f4be-7c02-4c33-a44a-e90213f893f1","pdf_url":"https://discovery.dundee.ac.uk/ws/files/51734058/SymmetryCod2Aggmodels_Buono_Eftimie_SIADS_FinalVersion.pdf","source":{"id":"https://openalex.org/S4306400523","display_name":"Discovery Research Portal (University of Dundee)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I177639307","host_organization_name":"University of Dundee","host_organization_lineage":["https://openalex.org/I177639307"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Buono, P-L & Eftimie, R 2014, 'Codimension-two bifurcations in animal aggregation models with symmetry', Siam Journal on Applied Dynamical Systems, vol. 13, no. 4, pp. 1542-1582. https://doi.org/10.1137/130932272","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:discovery.dundee.ac.uk:openaire/58f0f4be-7c02-4c33-a44a-e90213f893f1","is_oa":true,"landing_page_url":"https://discovery.dundee.ac.uk/en/publications/58f0f4be-7c02-4c33-a44a-e90213f893f1","pdf_url":"https://discovery.dundee.ac.uk/ws/files/51734058/SymmetryCod2Aggmodels_Buono_Eftimie_SIADS_FinalVersion.pdf","source":{"id":"https://openalex.org/S4306400523","display_name":"Discovery Research Portal (University of Dundee)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I177639307","host_organization_name":"University of Dundee","host_organization_lineage":["https://openalex.org/I177639307"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Buono, P-L & Eftimie, R 2014, 'Codimension-two bifurcations in animal aggregation models with symmetry', Siam Journal on Applied Dynamical Systems, vol. 13, no. 4, pp. 1542-1582. https://doi.org/10.1137/130932272","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2165548363","display_name":null,"funder_award_id":"Canada","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G2998137668","display_name":null,"funder_award_id":"unknown","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G400116904","display_name":null,"funder_award_id":"unknow","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G6646366205","display_name":null,"funder_award_id":"EP/K033689/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8452545418","display_name":null,"funder_award_id":"unknown","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2138385728.pdf","grobid_xml":"https://content.openalex.org/works/W2138385728.grobid-xml"},"referenced_works_count":47,"referenced_works":["https://openalex.org/W645587989","https://openalex.org/W1580229328","https://openalex.org/W1734689372","https://openalex.org/W1965778005","https://openalex.org/W1977892515","https://openalex.org/W1986790793","https://openalex.org/W1997795840","https://openalex.org/W2002581511","https://openalex.org/W2006175264","https://openalex.org/W2010017500","https://openalex.org/W2011374157","https://openalex.org/W2011942344","https://openalex.org/W2014344946","https://openalex.org/W2015908665","https://openalex.org/W2025801169","https://openalex.org/W2032024857","https://openalex.org/W2039313558","https://openalex.org/W2044680442","https://openalex.org/W2047957002","https://openalex.org/W2049042517","https://openalex.org/W2052946502","https://openalex.org/W2062959567","https://openalex.org/W2063491472","https://openalex.org/W2067035389","https://openalex.org/W2071304811","https://openalex.org/W2083350922","https://openalex.org/W2089714094","https://openalex.org/W2090583502","https://openalex.org/W2097490641","https://openalex.org/W2100154176","https://openalex.org/W2110116716","https://openalex.org/W2112164016","https://openalex.org/W2117279095","https://openalex.org/W2119414533","https://openalex.org/W2126912356","https://openalex.org/W2129823023","https://openalex.org/W2143969246","https://openalex.org/W2151330722","https://openalex.org/W2155242093","https://openalex.org/W2155385278","https://openalex.org/W2167052694","https://openalex.org/W2169218999","https://openalex.org/W2176984061","https://openalex.org/W2331625639","https://openalex.org/W2333623808","https://openalex.org/W2336126179","https://openalex.org/W2757330548"],"related_works":["https://openalex.org/W1861797342","https://openalex.org/W2950310075","https://openalex.org/W2532296123","https://openalex.org/W2378750705","https://openalex.org/W2356579025","https://openalex.org/W2783068836","https://openalex.org/W2801648456","https://openalex.org/W2070969328","https://openalex.org/W2099381872","https://openalex.org/W2093411828"],"abstract_inverted_index":{"Pattern":[0],"formation":[1,25],"in":[2],"self-organized":[3,104],"biological":[4,31,55,194],"aggregation":[5],"is":[6,45],"a":[7,97],"phenomenon":[8],"that":[9,33,57,80,108,134],"has":[10],"been":[11],"studied":[12],"intensively":[13],"over":[14],"the":[15,21,30,39,54,61,67,78,129,150,162,174,188,193],"past":[16],"20":[17],"years.":[18],"In":[19,91],"general,":[20],"studies":[22],"on":[23,28,53,77,96],"pattern":[24],"focus":[26,95],"mainly":[27],"identifying":[29,38],"mechanisms":[32,41,79],"generate":[34],"these":[35,43,109,177],"patterns.":[36,71],"However,":[37],"mathematical":[40],"behind":[42],"patterns":[44,65,85,133],"equally":[46],"important,":[47],"since":[48],"it":[49,73],"can":[50,74],"offer":[51,75],"information":[52,76],"parameters":[56],"could":[58],"contribute":[59],"to":[60,127,154],"persistence":[62],"of":[63,69,99,132,166,169,176,182,196],"some":[64],"and":[66,106,124,144,159,164,179],"disappearance":[68],"other":[70],"Also,":[72,185],"trigger":[81],"transitions":[82,197],"between":[83,198],"different":[84,88,199],"(associated":[86],"with":[87],"group":[89,200],"behaviors).":[90],"this":[92],"article,":[93],"we":[94,160,186],"class":[98],"nonlocal":[100],"hyperbolic":[101],"models":[102,110],"for":[103],"aggregations":[105],"show":[107,173],"are":[111],"${{\\bf":[112,137],"O(2)}}$-equivariant.":[113],"We":[114,148,171],"then":[115],"use":[116],"group-theoretic":[117],"methods,":[118],"linear":[119],"analysis,":[120,123],"weakly":[121],"nonlinear":[122],"numerical":[125],"simulations":[126],"investigate":[128],"large":[130],"variety":[131],"arise":[135],"through":[136],"O(2)}}$-symmetric":[138],"codimension-two":[139],"bifurcations":[140],"(i.e.,":[141],"Hopf/Hopf,":[142],"steady-state/Hopf,":[143],"steady-state/steady-state":[145],"mode":[146],"interactions).":[147],"classify":[149],"bifurcating":[151,190],"solutions":[152,178,191],"according":[153],"their":[155],"isotropy":[156],"types":[157],"(subgroups),":[158],"determine":[161,180],"criticality":[163],"stability":[165],"primary":[167],"branches":[168],"solutions.":[170],"numerically":[172],"existence":[175],"scenarios":[181],"secondary":[183,189],"bifurcations.":[184],"discuss":[187],"from":[192],"perspective":[195],"behaviors.":[201]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-14T08:04:32.555800","created_date":"2025-10-10T00:00:00"}
