{"id":"https://openalex.org/W3026931092","doi":"https://doi.org/10.1137/20m1339003","title":"Rate-Induced Tipping and Saddle-Node Bifurcation for Quadratic Differential Equations with Nonautonomous Asymptotic Dynamics","display_name":"Rate-Induced Tipping and Saddle-Node Bifurcation for Quadratic Differential Equations with Nonautonomous Asymptotic Dynamics","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3026931092","doi":"https://doi.org/10.1137/20m1339003","mag":"3026931092"},"language":"en","primary_location":{"id":"doi:10.1137/20m1339003","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1339003","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2110.02608","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Iacopo P. Longo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Iacopo P. Longo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Carmen N\u00fan\u0342ez","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Carmen N\u00fan\u0342ez","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Rafael Obaya","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rafael Obaya","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Martin Rasmussen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Martin Rasmussen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3696,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.78486952,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":99},"biblio":{"volume":"20","issue":"1","first_page":"500","last_page":"540"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13377","display_name":"Ecosystem dynamics and resilience","score":0.82669997215271,"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"}},"topics":[{"id":"https://openalex.org/T13377","display_name":"Ecosystem dynamics and resilience","score":0.82669997215271,"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"}},{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.06700000166893005,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.02979999966919422,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/bounded-function","display_name":"Bounded function","score":0.6711999773979187},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5511999726295471},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5180000066757202},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.5005000233650208},{"id":"https://openalex.org/keywords/delay-differential-equation","display_name":"Delay differential equation","score":0.44110000133514404},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.43860000371932983},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.42719998955726624},{"id":"https://openalex.org/keywords/uniform-boundedness","display_name":"Uniform boundedness","score":0.37380000948905945},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.3488999903202057}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7541999816894531},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6711999773979187},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6118000149726868},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5511999726295471},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5180000066757202},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.5005000233650208},{"id":"https://openalex.org/C147504518","wikidata":"https://www.wikidata.org/wiki/Q2146125","display_name":"Delay differential equation","level":3,"score":0.44110000133514404},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.43860000371932983},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.42719998955726624},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.37380000948905945},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.3488999903202057},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.3409999907016754},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.3147999942302704},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.31150001287460327},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.3084000051021576},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.30410000681877136},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.2976999878883362},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.2930999994277954},{"id":"https://openalex.org/C110521144","wikidata":"https://www.wikidata.org/wiki/Q193460","display_name":"Scalar field","level":2,"score":0.28999999165534973},{"id":"https://openalex.org/C2778433361","wikidata":"https://www.wikidata.org/wiki/Q7268358","display_name":"Quadratic differential","level":3,"score":0.28110000491142273},{"id":"https://openalex.org/C205147927","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic analysis","level":2,"score":0.2766999900341034},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.2736000120639801},{"id":"https://openalex.org/C185184677","wikidata":"https://www.wikidata.org/wiki/Q1366795","display_name":"Exact differential equation","level":4,"score":0.2694000005722046},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.263700008392334},{"id":"https://openalex.org/C181154966","wikidata":"https://www.wikidata.org/wiki/Q2500406","display_name":"Li\u00e9nard equation","level":5,"score":0.2554999887943268},{"id":"https://openalex.org/C9628104","wikidata":"https://www.wikidata.org/wiki/Q788009","display_name":"Autonomous system (mathematics)","level":2,"score":0.25209999084472656}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/20m1339003","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1339003","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:arXiv.org:2110.02608","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2110.02608","pdf_url":"https://arxiv.org/pdf/2110.02608","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:spiral.imperial.ac.uk:10044/1/86439","is_oa":false,"landing_page_url":"http://hdl.handle.net/10044/1/86439","pdf_url":null,"source":{"id":"https://openalex.org/S4306401396","display_name":"Spiral (Imperial College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I47508984","host_organization_name":"Imperial College London","host_organization_lineage":["https://openalex.org/I47508984"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"540","raw_type":"Journal Article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2110.02608","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2110.02608","pdf_url":"https://arxiv.org/pdf/2110.02608","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G357887633","display_name":"International Network of Excellence in Science Technology","funder_award_id":"754462","funder_id":"https://openalex.org/F4320338337","funder_display_name":"H2020 Marie Sk\u0142odowska-Curie Actions"},{"id":"https://openalex.org/G3905470062","display_name":null,"funder_award_id":"RTI2018-096523-B-I00","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"},{"id":"https://openalex.org/G434337789","display_name":null,"funder_award_id":"HORIZON2020","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5997748000","display_name":"Critical Transitions in Complex Systems","funder_award_id":"643073","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G6205457372","display_name":"Critical Transitions in Complex Systems","funder_award_id":"643073","funder_id":"https://openalex.org/F4320338337","funder_display_name":"H2020 Marie Sk\u0142odowska-Curie Actions"},{"id":"https://openalex.org/G6845901740","display_name":"International Network of Excellence in Science Technology","funder_award_id":"754462","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8181105605","display_name":null,"funder_award_id":"RTI2018","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"}],"funders":[{"id":"https://openalex.org/F4320315062","display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","ror":null},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320338337","display_name":"H2020 Marie Sk\u0142odowska-Curie Actions","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1490150044","https://openalex.org/W1547667045","https://openalex.org/W1971224475","https://openalex.org/W2011169631","https://openalex.org/W2025881996","https://openalex.org/W2027236411","https://openalex.org/W2030350658","https://openalex.org/W2032318686","https://openalex.org/W2049736198","https://openalex.org/W2081128244","https://openalex.org/W2109403803","https://openalex.org/W2134761831","https://openalex.org/W2163412959","https://openalex.org/W2316220071","https://openalex.org/W2331787088","https://openalex.org/W2746628645","https://openalex.org/W2914114415","https://openalex.org/W2957355446","https://openalex.org/W2963540800"],"related_works":[],"abstract_inverted_index":{"An":[0],"in-depth":[1],"analysis":[2],"of":[3,6,35,95],"nonautonomous":[4],"bifurcations":[5],"saddle-node":[7],"type":[8],"for":[9,38,57,63,68],"scalar":[10],"differential":[11,40],"equations":[12],"$x'=-x^2+q(t)\\,x+p(t)$,":[13],"where":[14],"$q\\colon\\mathbb":[15],"R\\to\\mathbb":[16,20],"R$":[17,21],"and":[18,24,92],"$p\\colon\\mathbb":[19],"are":[22],"bounded":[23],"uniformly":[25],"continuous,":[26],"is":[27,59],"fundamental":[28],"to":[29,76],"explaining":[30],"the":[31,39,45,93,96],"absence":[32],"or":[33,66],"occurrence":[34],"rate-induced":[36,77],"tipping":[37],"equation":[41],"$y'":[42],"=(y-(2/\\pi)\\arctan(ct))^2+p(t)$":[43],"as":[44],"rate":[46,72],"$c$":[47,103],"varies":[48],"on":[49],"$[0,\\infty)$.":[50],"A":[51,79],"classical":[52,97],"attractor-repeller":[53,98],"pair,":[54],"whose":[55],"existence":[56,94],"$c=0$":[58],"assumed,":[60],"may":[61,100],"persist":[62],"any":[64],"$c>0$,":[65],"disappear":[67],"a":[69],"certain":[70],"critical":[71,90],"$c=c_0$,":[73],"giving":[74],"rise":[75],"tipping.":[78],"suitable":[80],"example":[81],"demonstrates":[82],"that":[83],"one":[84,89],"can":[85],"have":[86],"more":[87],"than":[88],"rate,":[91],"pair":[99],"return":[101],"when":[102],"increases.":[104]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2020-05-29T00:00:00"}