{"id":"https://openalex.org/W2084703283","doi":"https://doi.org/10.1142/s0218127405013241","title":"BORDER COLLISION BIFURCATIONS IN THE EVOLUTION OF MUTUALISTIC INTERACTIONS","display_name":"BORDER COLLISION BIFURCATIONS IN THE EVOLUTION OF MUTUALISTIC INTERACTIONS","publication_year":2005,"publication_date":"2005-07-01","ids":{"openalex":"https://openalex.org/W2084703283","doi":"https://doi.org/10.1142/s0218127405013241","mag":"2084703283"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127405013241","is_oa":true,"landing_page_url":"https://doi.org/10.1142/s0218127405013241","pdf_url":"http://pure.iiasa.ac.at/id/eprint/7759/1/IR-05-083.pdf","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":true,"oa_status":"bronze","oa_url":"http://pure.iiasa.ac.at/id/eprint/7759/1/IR-05-083.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069148682","display_name":"Fabio Dercole","orcid":"https://orcid.org/0000-0001-9256-0651"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"FABIO DERCOLE","raw_affiliation_strings":["DEI, Politecnico di Milano, Via Ponzio 34/5, 20133 Milano, Italy","DEI Politecnico di Milano, Via Ponzio 34/5, 20133 Milano, Italy#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DEI, Politecnico di Milano, Via Ponzio 34/5, 20133 Milano, Italy","institution_ids":["https://openalex.org/I93860229"]},{"raw_affiliation_string":"DEI Politecnico di Milano, Via Ponzio 34/5, 20133 Milano, Italy#TAB#","institution_ids":["https://openalex.org/I93860229"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5069148682"],"corresponding_institution_ids":["https://openalex.org/I93860229"],"apc_list":null,"apc_paid":null,"fwci":0.3566,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.64782145,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"15","issue":"07","first_page":"2179","last_page":"2190"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11764","display_name":"Evolution and Genetic Dynamics","score":0.9994000196456909,"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":0.9994000196456909,"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9980999827384949,"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":0.9979000091552734,"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/collision","display_name":"Collision","score":0.6344705820083618},{"id":"https://openalex.org/keywords/trait","display_name":"Trait","score":0.6299684643745422},{"id":"https://openalex.org/keywords/evolutionary-dynamics","display_name":"Evolutionary dynamics","score":0.5942065715789795},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4909077286720276},{"id":"https://openalex.org/keywords/adaptive-value","display_name":"Adaptive value","score":0.47397369146347046},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4447011351585388},{"id":"https://openalex.org/keywords/extinction","display_name":"Extinction (optical mineralogy)","score":0.41452592611312866},{"id":"https://openalex.org/keywords/evolutionary-biology","display_name":"Evolutionary biology","score":0.37159931659698486},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3620678186416626},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.32967448234558105},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.3291434049606323},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29770755767822266},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17253929376602173},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1054915189743042}],"concepts":[{"id":"https://openalex.org/C121704057","wikidata":"https://www.wikidata.org/wiki/Q352070","display_name":"Collision","level":2,"score":0.6344705820083618},{"id":"https://openalex.org/C106934330","wikidata":"https://www.wikidata.org/wiki/Q1971873","display_name":"Trait","level":2,"score":0.6299684643745422},{"id":"https://openalex.org/C171578705","wikidata":"https://www.wikidata.org/wiki/Q5418700","display_name":"Evolutionary dynamics","level":3,"score":0.5942065715789795},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4909077286720276},{"id":"https://openalex.org/C88654294","wikidata":"https://www.wikidata.org/wiki/Q4680775","display_name":"Adaptive value","level":2,"score":0.47397369146347046},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4447011351585388},{"id":"https://openalex.org/C101991246","wikidata":"https://www.wikidata.org/wiki/Q5422078","display_name":"Extinction (optical mineralogy)","level":2,"score":0.41452592611312866},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.37159931659698486},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3620678186416626},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.32967448234558105},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.3291434049606323},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29770755767822266},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17253929376602173},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1054915189743042},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"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":3,"locations":[{"id":"doi:10.1142/s0218127405013241","is_oa":true,"landing_page_url":"https://doi.org/10.1142/s0218127405013241","pdf_url":"http://pure.iiasa.ac.at/id/eprint/7759/1/IR-05-083.pdf","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"},{"id":"pmh:oai:pure.iiasa.ac.at:7759","is_oa":false,"landing_page_url":"http://pure.iiasa.ac.at/id/eprint/7759/1/IR-05-083.pdf","pdf_url":"http://pure.iiasa.ac.at/id/eprint/7759/1/IR-05-083.pdf","source":{"id":"https://openalex.org/S4306401423","display_name":"IIASA PURE (International Institute of Applied Systems Analysis)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1317774081","host_organization_name":"International Institute for Applied Systems Analysis","host_organization_lineage":["https://openalex.org/I1317774081"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Monograph"},{"id":"pmh:oai:re.public.polimi.it:11311/554563","is_oa":false,"landing_page_url":"http://www.worldscientific.com/doi/abs/10.1142/S0218127405013241","pdf_url":null,"source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1142/s0218127405013241","is_oa":true,"landing_page_url":"https://doi.org/10.1142/s0218127405013241","pdf_url":"http://pure.iiasa.ac.at/id/eprint/7759/1/IR-05-083.pdf","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"},"sustainable_development_goals":[{"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15","score":0.47999998927116394}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321873","display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca","ror":"https://ror.org/0166hxq48"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2084703283.pdf","grobid_xml":"https://content.openalex.org/works/W2084703283.grobid-xml"},"referenced_works_count":72,"referenced_works":["https://openalex.org/W160832363","https://openalex.org/W1552094772","https://openalex.org/W1552686331","https://openalex.org/W1574004712","https://openalex.org/W1589520441","https://openalex.org/W1592648094","https://openalex.org/W1596227557","https://openalex.org/W1596321532","https://openalex.org/W1606282725","https://openalex.org/W1765868291","https://openalex.org/W1965780536","https://openalex.org/W1968415792","https://openalex.org/W1971253284","https://openalex.org/W1974520525","https://openalex.org/W1981246608","https://openalex.org/W1983736546","https://openalex.org/W1986738940","https://openalex.org/W1990042683","https://openalex.org/W1999916297","https://openalex.org/W2006165838","https://openalex.org/W2011227277","https://openalex.org/W2013456332","https://openalex.org/W2017464661","https://openalex.org/W2017478823","https://openalex.org/W2017479337","https://openalex.org/W2017880973","https://openalex.org/W2028435430","https://openalex.org/W2031604902","https://openalex.org/W2033706714","https://openalex.org/W2035791902","https://openalex.org/W2039305628","https://openalex.org/W2040131740","https://openalex.org/W2040269786","https://openalex.org/W2041554853","https://openalex.org/W2041666350","https://openalex.org/W2046942447","https://openalex.org/W2047449028","https://openalex.org/W2049319278","https://openalex.org/W2059380896","https://openalex.org/W2060338694","https://openalex.org/W2062663664","https://openalex.org/W2068536407","https://openalex.org/W2074300851","https://openalex.org/W2079033018","https://openalex.org/W2082760914","https://openalex.org/W2084253034","https://openalex.org/W2088238658","https://openalex.org/W2091198440","https://openalex.org/W2094734627","https://openalex.org/W2098044557","https://openalex.org/W2099385429","https://openalex.org/W2104291321","https://openalex.org/W2107411326","https://openalex.org/W2128569550","https://openalex.org/W2140124925","https://openalex.org/W2140611459","https://openalex.org/W2143557716","https://openalex.org/W2149884362","https://openalex.org/W2157813453","https://openalex.org/W2159251357","https://openalex.org/W2163668399","https://openalex.org/W2164761951","https://openalex.org/W2167401140","https://openalex.org/W2883512297","https://openalex.org/W4205749261","https://openalex.org/W4206651839","https://openalex.org/W4230906466","https://openalex.org/W4238000550","https://openalex.org/W4241044936","https://openalex.org/W4243549040","https://openalex.org/W4293078920","https://openalex.org/W4300750523"],"related_works":["https://openalex.org/W2166775973","https://openalex.org/W1990670209","https://openalex.org/W2096701021","https://openalex.org/W2346752865","https://openalex.org/W2936425165","https://openalex.org/W4323804398","https://openalex.org/W2303767852","https://openalex.org/W2328847973","https://openalex.org/W2010039647","https://openalex.org/W3104400618"],"abstract_inverted_index":{"The":[0,41,114,132],"paper":[1],"describes":[2],"the":[3,12,30,32,44,66,85,108,111,138],"slow":[4],"evolution":[5],"of":[6,29,43,54,61,77,88,110,116,127],"two":[7,15,33,125],"adaptive":[8],"traits":[9,45],"that":[10],"regulate":[11],"interactions":[13],"between":[14],"mutualistic":[16],"populations":[17,34,48],"(e.g.":[18],"a":[19,74,101],"flowering":[20],"plant":[21],"and":[22,118,134],"its":[23],"insect":[24],"pollinator).":[25],"For":[26],"frozen":[27],"values":[28,42],"traits,":[31],"can":[35],"either":[36],"coexist":[37],"or":[38],"go":[39],"extinct.":[40],"for":[46],"which":[47,80],"extinction":[49],"is":[50,81,130],"guaranteed":[51],"are":[52,142],"therefore":[53],"no":[55],"interest":[56,129],"from":[57],"an":[58],"evolutionary":[59,67,93],"point":[60],"view.":[62],"In":[63],"other":[64],"words,":[65],"dynamics":[68,94],"must":[69],"be":[70],"studied":[71],"only":[72],"in":[73,104],"viable":[75,112],"subset":[76],"trait":[78,90,105],"space,":[79],"bounded":[82],"due":[83],"to":[84,124],"physiological":[86],"cost":[87],"extreme":[89],"values.":[91],"Thus,":[92],"experience":[95],"so-called":[96],"border":[97,109,119,139],"collision":[98,120,140],"bifurcations,":[99],"when":[100],"system":[102],"invariant":[103],"space":[106],"hits":[107],"subset.":[113],"unfolding":[115],"standard":[117],"bifurcations":[121,141],"with":[122,145],"respect":[123],"parameters":[126],"biological":[128],"presented.":[131],"algebraic":[133],"boundary-value":[135],"problems":[136],"characterizing":[137],"described":[143],"together":[144],"some":[146],"details":[147],"concerning":[148],"their":[149],"computation.":[150]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-19T15:00:24.278416","created_date":"2025-10-10T00:00:00"}
