{"id":"https://openalex.org/W4393050376","doi":"https://doi.org/10.1142/s0218127424500457","title":"Functional Shift-Induced Degenerate Transcritical Neimark\u2013Sacker Bifurcation in a Discrete Hypercycle","display_name":"Functional Shift-Induced Degenerate Transcritical Neimark\u2013Sacker Bifurcation in a Discrete Hypercycle","publication_year":2024,"publication_date":"2024-03-20","ids":{"openalex":"https://openalex.org/W4393050376","doi":"https://doi.org/10.1142/s0218127424500457"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127424500457","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1142/s0218127424500457","pdf_url":null,"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":"green","oa_url":"https://upcommons.upc.edu/bitstreams/c7ede58c-fba5-4688-af27-d6718b91c870/download","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085608480","display_name":"Ernest Fontich","orcid":"https://orcid.org/0000-0002-2415-9310"},"institutions":[{"id":"https://openalex.org/I4210122226","display_name":"Centre de Recerca Matem\u00e0tica","ror":"https://ror.org/020s51w82","country_code":"ES","type":"facility","lineage":["https://openalex.org/I4210122226","https://openalex.org/I4387153040"]},{"id":"https://openalex.org/I71999127","display_name":"Universitat de Barcelona","ror":"https://ror.org/021018s57","country_code":"ES","type":"education","lineage":["https://openalex.org/I71999127"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Ernest Fontich","raw_affiliation_strings":["Centre de Recerca Matem\u00e0tica (CRM), Cerdanyola del Vall\u00e8s, 08193 Barcelona, Catalonia, Spain","Departament de Matem\u00e0tiques i Inform\u00e0tica, Universitat de Barcelona (UB), Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain"],"raw_orcid":"https://orcid.org/0000-0002-2415-9310","affiliations":[{"raw_affiliation_string":"Centre de Recerca Matem\u00e0tica (CRM), Cerdanyola del Vall\u00e8s, 08193 Barcelona, Catalonia, Spain","institution_ids":["https://openalex.org/I4210122226"]},{"raw_affiliation_string":"Departament de Matem\u00e0tiques i Inform\u00e0tica, Universitat de Barcelona (UB), Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain","institution_ids":["https://openalex.org/I71999127"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071471988","display_name":"Antoni Guillamon","orcid":"https://orcid.org/0000-0001-8268-4503"},"institutions":[{"id":"https://openalex.org/I4210122226","display_name":"Centre de Recerca Matem\u00e0tica","ror":"https://ror.org/020s51w82","country_code":"ES","type":"facility","lineage":["https://openalex.org/I4210122226","https://openalex.org/I4387153040"]},{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Antoni Guillamon","raw_affiliation_strings":["Centre de Recerca Matem\u00e0tica (CRM), Cerdanyola del Vall\u00e8s, 08193 Barcelona, Catalonia, Spain","Departament de Matem\u00e0tiques and IMTech, Universitat Polit\u00e8cnica de Catalunya, EPSEB, Av. Dr. Mara\u00f1\u00f3n 44-50, 08028 Barcelona, Catalonia, Spain"],"raw_orcid":"https://orcid.org/0000-0001-8268-4503","affiliations":[{"raw_affiliation_string":"Centre de Recerca Matem\u00e0tica (CRM), Cerdanyola del Vall\u00e8s, 08193 Barcelona, Catalonia, Spain","institution_ids":["https://openalex.org/I4210122226"]},{"raw_affiliation_string":"Departament de Matem\u00e0tiques and IMTech, Universitat Polit\u00e8cnica de Catalunya, EPSEB, Av. Dr. Mara\u00f1\u00f3n 44-50, 08028 Barcelona, Catalonia, Spain","institution_ids":["https://openalex.org/I9617848"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023882836","display_name":"J\u00falia Perona","orcid":null},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"J\u00falia Perona","raw_affiliation_strings":["Departament de Matem\u00e0tiques, Universitat Polit\u00e8cnica de Catalunya, EPSEB, Av. Dr. Mara\u00f1\u00f3n 44-50, 08028 Barcelona, Catalonia, Spain"],"raw_orcid":"https://orcid.org/0009-0005-4154-5917","affiliations":[{"raw_affiliation_string":"Departament de Matem\u00e0tiques, Universitat Polit\u00e8cnica de Catalunya, EPSEB, Av. Dr. Mara\u00f1\u00f3n 44-50, 08028 Barcelona, Catalonia, Spain","institution_ids":["https://openalex.org/I9617848"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022876719","display_name":"Josep Sardany\u00e9s","orcid":null},"institutions":[{"id":"https://openalex.org/I4210122226","display_name":"Centre de Recerca Matem\u00e0tica","ror":"https://ror.org/020s51w82","country_code":"ES","type":"facility","lineage":["https://openalex.org/I4210122226","https://openalex.org/I4387153040"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Josep Sardany\u00e9s","raw_affiliation_strings":["Centre de Recerca Matem\u00e0tica (CRM), Cerdanyola del Vall\u00e8s, 08193 Barcelona, Catalonia, Spain"],"raw_orcid":"https://orcid.org/0000-0001-7225-5158","affiliations":[{"raw_affiliation_string":"Centre de Recerca Matem\u00e0tica (CRM), Cerdanyola del Vall\u00e8s, 08193 Barcelona, Catalonia, Spain","institution_ids":["https://openalex.org/I4210122226"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5085608480"],"corresponding_institution_ids":["https://openalex.org/I4210122226","https://openalex.org/I71999127"],"apc_list":null,"apc_paid":null,"fwci":0.9538,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.6689908,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"34","issue":"04","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9783999919891357,"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"}},"topics":[{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9783999919891357,"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"}},{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9764000177383423,"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"}},{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9616000056266785,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.6422534584999084},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.4496946930885315},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.432468056678772},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.41718384623527527},{"id":"https://openalex.org/keywords/transcritical-bifurcation","display_name":"Transcritical bifurcation","score":0.4112570285797119},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.3369746804237366},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32470405101776123},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.22351109981536865},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.13793054223060608}],"concepts":[{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.6422534584999084},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.4496946930885315},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.432468056678772},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.41718384623527527},{"id":"https://openalex.org/C55610538","wikidata":"https://www.wikidata.org/wiki/Q1502581","display_name":"Transcritical bifurcation","level":5,"score":0.4112570285797119},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.3369746804237366},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32470405101776123},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.22351109981536865},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.13793054223060608}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127424500457","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1142/s0218127424500457","pdf_url":null,"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:upcommons.upc.edu:2117/407258","is_oa":true,"landing_page_url":"https://hdl.handle.net/2117/407258","pdf_url":"https://upcommons.upc.edu/bitstreams/c7ede58c-fba5-4688-af27-d6718b91c870/download","source":{"id":"https://openalex.org/S4377196262","display_name":"UPCommons institutional repository (Universitat Polit\u00e8cnica de Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I9617848","host_organization_name":"Universitat Polit\u00e8cnica de Catalunya","host_organization_lineage":["https://openalex.org/I9617848"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:upcommons.upc.edu:2117/407258","is_oa":true,"landing_page_url":"https://hdl.handle.net/2117/407258","pdf_url":"https://upcommons.upc.edu/bitstreams/c7ede58c-fba5-4688-af27-d6718b91c870/download","source":{"id":"https://openalex.org/S4377196262","display_name":"UPCommons institutional repository (Universitat Polit\u00e8cnica de Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I9617848","host_organization_name":"Universitat Polit\u00e8cnica de Catalunya","host_organization_lineage":["https://openalex.org/I9617848"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"score":0.4099999964237213,"id":"https://metadata.un.org/sdg/17","display_name":"Partnerships for the goals"}],"awards":[{"id":"https://openalex.org/G1185443288","display_name":null,"funder_award_id":"MCIN/AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"},{"id":"https://openalex.org/G121809054","display_name":null,"funder_award_id":"MCIN/AEI/10","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G1281928558","display_name":null,"funder_award_id":"101003777","funder_id":"https://openalex.org/F4320318789","funder_display_name":"Biodiversa+"},{"id":"https://openalex.org/G1622782223","display_name":null,"funder_award_id":"MCIN/AEI/10","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G1643949827","display_name":null,"funder_award_id":"AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G181518970","display_name":null,"funder_award_id":"RYC-2017-22243","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G195474297","display_name":null,"funder_award_id":"2017-","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G2064873908","display_name":null,"funder_award_id":"10.13039/501100011033","funder_id":"https://openalex.org/F4320321505","funder_display_name":"Generalitat de Catalunya"},{"id":"https://openalex.org/G2092432181","display_name":null,"funder_award_id":"PID2021-125535NB-I00","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G2262748287","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G2309174360","display_name":null,"funder_award_id":"10.13039","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G2601397997","display_name":null,"funder_award_id":"10.13039/501100011033","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G2638770737","display_name":null,"funder_award_id":"2021SGR1039","funder_id":"https://openalex.org/F4320334830","funder_display_name":"Ag\u00e8ncia de Gesti\u00f3 d'Ajuts Universitaris i de Recerca"},{"id":"https://openalex.org/G288263039","display_name":null,"funder_award_id":"10.13039/501100011033","funder_id":"https://openalex.org/F4320334830","funder_display_name":"Ag\u00e8ncia de Gesti\u00f3 d'Ajuts Universitaris i de Recerca"},{"id":"https://openalex.org/G2936937667","display_name":"Promoting & implementing joint programming to reinforce transnational research for the conservation and restoration of degraded ecosystems and their biodiversity, including a focus on aquatic systems","funder_award_id":"101003777","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G3005324705","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320321505","funder_display_name":"Generalitat de Catalunya"},{"id":"https://openalex.org/G300979063","display_name":null,"funder_award_id":"10.13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G3150370218","display_name":null,"funder_award_id":"PCI2022-132926","funder_id":"https://openalex.org/F4320322579","funder_display_name":"Naturv\u00e5rdsverket"},{"id":"https://openalex.org/G3219925899","display_name":null,"funder_award_id":"MCIN/AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G3283673685","display_name":null,"funder_award_id":"PID-2021-122954NB-I00","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G3417140244","display_name":null,"funder_award_id":"CEX2020-001084-M","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G3480869486","display_name":null,"funder_award_id":"13039","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G3681454997","display_name":null,"funder_award_id":"13039/501100011033","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G4017095837","display_name":null,"funder_award_id":"AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G4042783231","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G4043177806","display_name":null,"funder_award_id":"101003777","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G4045093968","display_name":null,"funder_award_id":"MCIN/AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G410571670","display_name":null,"funder_award_id":"10.13039/501100011033","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G451917667","display_name":null,"funder_award_id":"13039/501100011033","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G4725750110","display_name":null,"funder_award_id":"101003777","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"},{"id":"https://openalex.org/G4976336944","display_name":null,"funder_award_id":"MCIN/AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320321505","funder_display_name":"Generalitat de Catalunya"},{"id":"https://openalex.org/G5080475149","display_name":null,"funder_award_id":"10.13039","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G5344670865","display_name":null,"funder_award_id":"PCI2022-132926","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G5421974903","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G5539308778","display_name":null,"funder_award_id":"AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G5550858994","display_name":null,"funder_award_id":"AEI/10","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G5852091828","display_name":null,"funder_award_id":"13039/501100011033","funder_id":"https://openalex.org/F4320334830","funder_display_name":"Ag\u00e8ncia de Gesti\u00f3 d'Ajuts Universitaris i de Recerca"},{"id":"https://openalex.org/G5860924931","display_name":null,"funder_award_id":"MCIN/AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320334830","funder_display_name":"Ag\u00e8ncia de Gesti\u00f3 d'Ajuts Universitaris i de Recerca"},{"id":"https://openalex.org/G5967599077","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G6283739012","display_name":null,"funder_award_id":"PID2021-125535NB-I00","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G6307970414","display_name":null,"funder_award_id":"CEX2020-001084-M","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G6325762137","display_name":null,"funder_award_id":"CEX2020-001084-M","funder_id":"https://openalex.org/F4320321505","funder_display_name":"Generalitat de Catalunya"},{"id":"https://openalex.org/G6415078851","display_name":null,"funder_award_id":"RYC-2017","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G6558061132","display_name":null,"funder_award_id":"MCIN/AEI/10.","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G6656126374","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320315803","funder_display_name":"Centres de Recerca de Catalunya"},{"id":"https://openalex.org/G6736728842","display_name":null,"funder_award_id":"PID2021-125535NB-I00","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G6744965099","display_name":null,"funder_award_id":"GA N\u00b0101003777","funder_id":"https://openalex.org/F4320318789","funder_display_name":"Biodiversa+"},{"id":"https://openalex.org/G6823456974","display_name":null,"funder_award_id":"AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G7084143925","display_name":null,"funder_award_id":"AEI/10","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G7186414377","display_name":null,"funder_award_id":"MCIN/AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G7266728691","display_name":null,"funder_award_id":"13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G7476827183","display_name":null,"funder_award_id":"CEX2020-001084-M","funder_id":"https://openalex.org/F4320315803","funder_display_name":"Centres de Recerca de Catalunya"},{"id":"https://openalex.org/G7535663061","display_name":null,"funder_award_id":"AEI/10.","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G7643708868","display_name":null,"funder_award_id":"10.13039/501100011033","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G7922897998","display_name":null,"funder_award_id":"MCIN/AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320322579","funder_display_name":"Naturv\u00e5rdsverket"},{"id":"https://openalex.org/G8055432103","display_name":null,"funder_award_id":"13039/501100011033","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G84477964","display_name":null,"funder_award_id":"CEX2020-001084-M","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G8452293441","display_name":null,"funder_award_id":"2020-2021","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8637226926","display_name":null,"funder_award_id":"MCIN/AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320315803","funder_display_name":"Centres de Recerca de Catalunya"},{"id":"https://openalex.org/G8680091935","display_name":null,"funder_award_id":"2020-2021","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G8695128545","display_name":null,"funder_award_id":"MCIN/AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8853601691","display_name":null,"funder_award_id":"/AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G8872346354","display_name":null,"funder_award_id":"MCIN/AEI/10.13039","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G8920660035","display_name":null,"funder_award_id":"PID2022","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"}],"funders":[{"id":"https://openalex.org/F4320313796","display_name":"Innovationsfonden","ror":"https://ror.org/00daj4111"},{"id":"https://openalex.org/F4320314162","display_name":"Joint Programming Initiative Water challenges for a changing world","ror":null},{"id":"https://openalex.org/F4320315803","display_name":"Centres de Recerca de Catalunya","ror":null},{"id":"https://openalex.org/F4320318789","display_name":"Biodiversa+","ror":"https://ror.org/05cvqmv08"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320321505","display_name":"Generalitat de Catalunya","ror":"https://ror.org/01bg62x04"},{"id":"https://openalex.org/F4320322579","display_name":"Naturv\u00e5rdsverket","ror":"https://ror.org/02y7nf053"},{"id":"https://openalex.org/F4320322930","display_name":"Ministerio de Ciencia e Innovaci\u00f3n","ror":"https://ror.org/034900433"},{"id":"https://openalex.org/F4320334779","display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","ror":"https://ror.org/00snfqn58"},{"id":"https://openalex.org/F4320334830","display_name":"Ag\u00e8ncia de Gesti\u00f3 d'Ajuts Universitaris i de Recerca","ror":"https://ror.org/01n4pqe45"},{"id":"https://openalex.org/F4320335322","display_name":"European Regional Development Fund","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":null}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4393050376.pdf"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W1965756628","https://openalex.org/W1967171923","https://openalex.org/W1975206443","https://openalex.org/W2021492857","https://openalex.org/W2024470488","https://openalex.org/W2029077390","https://openalex.org/W2040525210","https://openalex.org/W2055294127","https://openalex.org/W2068856213","https://openalex.org/W2069588772","https://openalex.org/W2073124368","https://openalex.org/W2078904661","https://openalex.org/W2086941802","https://openalex.org/W2087895317","https://openalex.org/W2097242917","https://openalex.org/W2106609868","https://openalex.org/W2130027567","https://openalex.org/W2169010693","https://openalex.org/W2182274314","https://openalex.org/W2335280132","https://openalex.org/W2579737313","https://openalex.org/W2767365591","https://openalex.org/W2793726990","https://openalex.org/W2963382137","https://openalex.org/W3000068290","https://openalex.org/W3009004209","https://openalex.org/W3099586756","https://openalex.org/W3191754518","https://openalex.org/W4205749261"],"related_works":["https://openalex.org/W257838698","https://openalex.org/W4296008178","https://openalex.org/W189436430","https://openalex.org/W2353805507","https://openalex.org/W2012700469","https://openalex.org/W2978811910","https://openalex.org/W2393929457","https://openalex.org/W2342467592","https://openalex.org/W3103157921","https://openalex.org/W2884051366"],"abstract_inverted_index":{"In":[0],"this":[1,38,97],"paper,":[2],"we":[3,106],"investigate":[4],"the":[5,17,24,34,79,84,108,111,116],"impact":[6],"of":[7,23,68,96,103,110],"functional":[8,39],"shifts":[9,26],"in":[10,61,86],"a":[11,28,31,46,62,69,87,92,101],"time-discrete":[12],"cross-catalytic":[13],"system.":[14],"We":[15,90],"use":[16],"hypercycle":[18],"model":[19],"considering":[20],"that":[21],"one":[22],"species":[25],"from":[27,115],"cooperator":[29],"to":[30,45,118],"degrader.":[32],"At":[33],"bifurcation":[35,80,85],"caused":[36],"by":[37],"shift,":[40],"an":[41],"invariant":[42,112],"curve":[43,113],"collapses":[44],"point":[47],"[Formula:":[48,58,72],"see":[49,59,73],"text]":[50,60,74],"while,":[51],"simultaneously,":[52],"two":[53],"fixed":[54,76],"points":[55,67,77],"collide":[56],"with":[57],"transcritical":[63],"bifurcation.":[64,99],"Moreover,":[65],"all":[66],"line":[70],"containing":[71],"become":[75],"at":[78,83],"and":[81],"only":[82],"degenerate":[88,98],"scenario.":[89],"provide":[91],"complete":[93],"analytical":[94],"description":[95],"As":[100],"result":[102],"our":[104],"study,":[105],"prove":[107],"existence":[109],"arising":[114],"transition":[117],"cooperation.":[119]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
