{"id":"https://openalex.org/W4402605127","doi":"https://doi.org/10.1007/s00332-024-10088-6","title":"Critical Transitions for Asymptotically Concave or d-Concave Nonautonomous Differential Equations with Applications in Ecology","display_name":"Critical Transitions for Asymptotically Concave or d-Concave Nonautonomous Differential Equations with Applications in Ecology","publication_year":2024,"publication_date":"2024-09-16","ids":{"openalex":"https://openalex.org/W4402605127","doi":"https://doi.org/10.1007/s00332-024-10088-6"},"language":"lv","primary_location":{"id":"doi:10.1007/s00332-024-10088-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00332-024-10088-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00332-024-10088-6.pdf","source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00332-024-10088-6.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064947104","display_name":"Jes\u00fas Garc\u00eda de Due\u00f1as","orcid":"https://orcid.org/0000-0001-8465-7621"},"institutions":[{"id":"https://openalex.org/I108103353","display_name":"Universidad de Valladolid","ror":"https://ror.org/01fvbaw18","country_code":"ES","type":"education","lineage":["https://openalex.org/I108103353"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Jes\u00fas Due\u00f1as","raw_affiliation_strings":["Departamento de Matem\u00e1tica Aplicada, Universidad de Valladolid, Paseo Prado de la Magdalena 3-5, 47011, Valladolid, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica Aplicada, Universidad de Valladolid, Paseo Prado de la Magdalena 3-5, 47011, Valladolid, Spain","institution_ids":["https://openalex.org/I108103353"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065951085","display_name":"Carmen N\u00fa\u00f1ez","orcid":"https://orcid.org/0000-0002-4344-6956"},"institutions":[{"id":"https://openalex.org/I108103353","display_name":"Universidad de Valladolid","ror":"https://ror.org/01fvbaw18","country_code":"ES","type":"education","lineage":["https://openalex.org/I108103353"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Carmen N\u00fa\u00f1ez","raw_affiliation_strings":["Departamento de Matem\u00e1tica Aplicada, Universidad de Valladolid, Paseo Prado de la Magdalena 3-5, 47011, Valladolid, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica Aplicada, Universidad de Valladolid, Paseo Prado de la Magdalena 3-5, 47011, Valladolid, Spain","institution_ids":["https://openalex.org/I108103353"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077559088","display_name":"Rafael Obaya","orcid":"https://orcid.org/0000-0003-1983-0402"},"institutions":[{"id":"https://openalex.org/I108103353","display_name":"Universidad de Valladolid","ror":"https://ror.org/01fvbaw18","country_code":"ES","type":"education","lineage":["https://openalex.org/I108103353"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Rafael Obaya","raw_affiliation_strings":["Departamento de Matem\u00e1tica Aplicada, Universidad de Valladolid, Paseo Prado de la Magdalena 3-5, 47011, Valladolid, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica Aplicada, Universidad de Valladolid, Paseo Prado de la Magdalena 3-5, 47011, Valladolid, Spain","institution_ids":["https://openalex.org/I108103353"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5065951085"],"corresponding_institution_ids":["https://openalex.org/I108103353"],"apc_list":{"value":3090,"currency":"USD","value_usd":3090},"apc_paid":{"value":3090,"currency":"USD","value_usd":3090},"fwci":1.1214,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.75392143,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"34","issue":"6","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13377","display_name":"Ecosystem dynamics and resilience","score":0.9997000098228455,"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":0.9997000098228455,"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9869999885559082,"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/T13811","display_name":"Earth Systems and Cosmic Evolution","score":0.9794999957084656,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5984524488449097},{"id":"https://openalex.org/keywords/concave-function","display_name":"Concave function","score":0.571734607219696},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4914807081222534},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.42998161911964417},{"id":"https://openalex.org/keywords/ecology","display_name":"Ecology","score":0.3661035895347595},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1962546706199646},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.1669693887233734},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.07529065012931824}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5984524488449097},{"id":"https://openalex.org/C66690126","wikidata":"https://www.wikidata.org/wiki/Q2914302","display_name":"Concave function","level":3,"score":0.571734607219696},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4914807081222534},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42998161911964417},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.3661035895347595},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1962546706199646},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.1669693887233734},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.07529065012931824}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00332-024-10088-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00332-024-10088-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00332-024-10088-6.pdf","source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"},{"id":"pmh:oai:uvadoc.uva.es:10324/69793","is_oa":true,"landing_page_url":"https://uvadoc.uva.es/handle/10324/69793","pdf_url":"https://uvadoc.uva.es/bitstream/10324/69793/4/critical_transitions_asymptotically_jns34.pdf","source":{"id":"https://openalex.org/S4306401553","display_name":"UVaDOC UVaDOC University of Valladolid Documentary Repository (University of Valladolid)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I108103353","host_organization_name":"Universidad de Valladolid","host_organization_lineage":["https://openalex.org/I108103353"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:uvadoc.uva.es:10324/69676","is_oa":true,"landing_page_url":"https://uvadoc.uva.es/handle/10324/69676","pdf_url":null,"source":{"id":"https://openalex.org/S4306400688","display_name":"University of Valladolid Documentary Repository (University of Valladolid)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I108103353","host_organization_name":"Universidad de Valladolid","host_organization_lineage":["https://openalex.org/I108103353"],"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":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s00332-024-10088-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00332-024-10088-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00332-024-10088-6.pdf","source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1319855363","display_name":null,"funder_award_id":"PIP-TCESC-2020","funder_id":"https://openalex.org/F4320324500","funder_display_name":"Universidad de Valladolid"},{"id":"https://openalex.org/G2287314818","display_name":null,"funder_award_id":"PID2021-125446NB-I00","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"},{"id":"https://openalex.org/G3103771800","display_name":null,"funder_award_id":"FPU20/01627","funder_id":"https://openalex.org/F7296444849","funder_display_name":"Ministerio de Universidades"},{"id":"https://openalex.org/G5864535684","display_name":null,"funder_award_id":"FPU20/01627","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/F4320324500","display_name":"Universidad de Valladolid","ror":"https://ror.org/01fvbaw18"},{"id":"https://openalex.org/F7296444849","display_name":"Ministerio de Universidades","ror":"https://ror.org/03zcny908"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4402605127.pdf","grobid_xml":"https://content.openalex.org/works/W4402605127.grobid-xml"},"referenced_works_count":45,"referenced_works":["https://openalex.org/W563254532","https://openalex.org/W657833124","https://openalex.org/W1533288419","https://openalex.org/W1547667045","https://openalex.org/W1967107766","https://openalex.org/W1969027200","https://openalex.org/W1971224475","https://openalex.org/W2011169631","https://openalex.org/W2011866841","https://openalex.org/W2030350658","https://openalex.org/W2049358805","https://openalex.org/W2083309269","https://openalex.org/W2116199452","https://openalex.org/W2130435784","https://openalex.org/W2133988428","https://openalex.org/W2134761831","https://openalex.org/W2163412959","https://openalex.org/W2330672085","https://openalex.org/W2746628645","https://openalex.org/W2895147355","https://openalex.org/W2914114415","https://openalex.org/W2939771715","https://openalex.org/W2964037860","https://openalex.org/W3000771293","https://openalex.org/W3026931092","https://openalex.org/W3083347222","https://openalex.org/W3094037338","https://openalex.org/W3104315032","https://openalex.org/W3106288355","https://openalex.org/W3121892360","https://openalex.org/W3183500276","https://openalex.org/W3204748347","https://openalex.org/W3214857526","https://openalex.org/W4205264027","https://openalex.org/W4239396084","https://openalex.org/W4255338393","https://openalex.org/W4282981785","https://openalex.org/W4292366057","https://openalex.org/W4309592436","https://openalex.org/W4323322332","https://openalex.org/W4323868056","https://openalex.org/W4386107952","https://openalex.org/W4387500742","https://openalex.org/W4389537403","https://openalex.org/W4392812769"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793","https://openalex.org/W4238204885"],"abstract_inverted_index":{"Abstract":[0],"The":[1,55,111,177],"occurrence":[2,186],"of":[3,107,118,142,154,174,187],"tracking":[4],"or":[5,141],"tipping":[6],"situations":[7],"for":[8,190],"a":[9,180],"transition":[10],"equation":[11],"$$x'=f(t,x,\\Gamma":[12,33,193],"(t,x))$$":[13,35,124,157],"x":[14,21,27,36,43,50,78,86,116,125,131,138,158,164,170,195,202,209],"\u2032":[15,37,196],"=":[16,38,89,197],"f":[17,39,127,160,198],"(":[18,24,40,47,73,75,83,128,135,161,167,199,206],"t":[19,25,41,48,69,76,84,129,136,162,168,200,207],",":[20,22,26,42,44,49,77,85,130,132,137,163,165,169,201,203,208],"\u0393":[23,45,74,81,133,166,204],")":[28,29,51,52,79,87,88,139,140,171,172,210,211],"with":[30,145],"asymptotic":[31,109],"limits":[32],"_\\pm":[34,66,123],"\u00b1":[46,71,82,134],"is":[53,58,99],"analyzed.":[54],"approaching":[56],"condition":[57],"just":[59],"$$\\lim":[60],"_{t\\rightarrow":[61],"\\pm":[62],"\\infty":[63],"}(\\Gamma":[64],"(t,x)-\\Gamma":[65],"(t,x))=0$$":[67],"lim":[68],"\u2192":[70],"\u221e":[72],"-":[80],"0":[90],"uniformly":[91],"on":[92,105],"compact":[93],"real":[94],"sets,":[95],"and":[96],"so":[97],"there":[98],"no":[100],"restriction":[101],"to":[102,147,183],"the":[103,108,119,148,185],"dependence":[104],"time":[106],"equations.":[110],"hypotheses":[112],"assume":[113],"concavity":[114],"in":[115],"either":[117],"maps":[120],"$$x\\mapsto":[121,155],"f(t,x,\\Gamma":[122,156],"\u21a6":[126,159],"their":[143],"derivatives":[144],"respect":[146],"state":[149],"variable":[150],"(d-concavity),":[151],"but":[152],"not":[153],"nor":[173],"its":[175],"derivative.":[176],"analysis":[178],"provides":[179],"powerful":[181],"tool":[182],"analyze":[184],"critical":[188],"transitions":[189],"one-parametric":[191],"families":[192],"^c(t,x))$$":[194],"c":[205],"</":[212]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1}],"updated_date":"2026-08-29T07:29:34.045763","created_date":"2024-09-19T00:00:00"}
