{"id":"https://openalex.org/W2472428923","doi":"https://doi.org/10.1007/s10208-017-9369-5","title":"Algorithm for Rigorous Integration of Delay Differential Equations and the Computer-Assisted Proof of Periodic Orbits in the Mackey\u2013Glass Equation","display_name":"Algorithm for Rigorous Integration of Delay Differential Equations and the Computer-Assisted Proof of Periodic Orbits in the Mackey\u2013Glass Equation","publication_year":2017,"publication_date":"2017-10-30","ids":{"openalex":"https://openalex.org/W2472428923","doi":"https://doi.org/10.1007/s10208-017-9369-5","mag":"2472428923"},"language":"en","primary_location":{"id":"doi:10.1007/s10208-017-9369-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-017-9369-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-017-9369-5.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"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":"Foundations of Computational Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10208-017-9369-5.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033277723","display_name":"Robert Szczelina","orcid":"https://orcid.org/0000-0001-7831-4577"},"institutions":[{"id":"https://openalex.org/I126596746","display_name":"Jagiellonian University","ror":"https://ror.org/03bqmcz70","country_code":"PL","type":"education","lineage":["https://openalex.org/I126596746"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Robert Szczelina","raw_affiliation_strings":["Ma\u0142opolska Center of Biotechnology, Jagiellonian University, Gronostajowa 7a, 30-374, Krak\u00f3w, Poland","Malopolska Center of Biotechnology Jagiellonian University Krakow Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ma\u0142opolska Center of Biotechnology, Jagiellonian University, Gronostajowa 7a, 30-374, Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I126596746"]},{"raw_affiliation_string":"Malopolska Center of Biotechnology Jagiellonian University Krakow Poland","institution_ids":["https://openalex.org/I126596746"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085109355","display_name":"Piotr Zgliczy\u0144ski","orcid":"https://orcid.org/0000-0002-4852-0887"},"institutions":[{"id":"https://openalex.org/I126596746","display_name":"Jagiellonian University","ror":"https://ror.org/03bqmcz70","country_code":"PL","type":"education","lineage":["https://openalex.org/I126596746"]},{"id":"https://openalex.org/I4210087266","display_name":"Institute of Computer Science","ror":"https://ror.org/003fvp964","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210087266","https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Piotr Zgliczy\u0144ski","raw_affiliation_strings":["Institute of Computer Science and Computational Mathematics, Jagiellonian University, \u0141ojasiewicza 6, 30-348, Krak\u00f3w, Poland","Institute of Computer Science and Computational Mathematics, Jagiellonian University, Krakow, Poland#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Computer Science and Computational Mathematics, Jagiellonian University, \u0141ojasiewicza 6, 30-348, Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I126596746","https://openalex.org/I4210087266"]},{"raw_affiliation_string":"Institute of Computer Science and Computational Mathematics, Jagiellonian University, Krakow, Poland#TAB#","institution_ids":["https://openalex.org/I126596746","https://openalex.org/I4210087266"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5033277723"],"corresponding_institution_ids":["https://openalex.org/I126596746"],"apc_list":{"value":2290,"currency":"USD","value_usd":2290},"apc_paid":{"value":2290,"currency":"USD","value_usd":2290},"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.00908826,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"18","issue":"6","first_page":"1299","last_page":"1332"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9803000092506409,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9803000092506409,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-assisted-proof","display_name":"Computer-assisted proof","score":0.8041881322860718},{"id":"https://openalex.org/keywords/delay-differential-equation","display_name":"Delay differential equation","score":0.7561845779418945},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.6059991717338562},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.6029427647590637},{"id":"https://openalex.org/keywords/periodic-orbits","display_name":"Periodic orbits","score":0.6012677550315857},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5443491339683533},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.44524848461151123},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.43515995144844055},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4239363372325897},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.35814741253852844},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22284460067749023},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19821399450302124},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1395111382007599}],"concepts":[{"id":"https://openalex.org/C173613240","wikidata":"https://www.wikidata.org/wiki/Q1150675","display_name":"Computer-assisted proof","level":3,"score":0.8041881322860718},{"id":"https://openalex.org/C147504518","wikidata":"https://www.wikidata.org/wiki/Q2146125","display_name":"Delay differential equation","level":3,"score":0.7561845779418945},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.6059991717338562},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.6029427647590637},{"id":"https://openalex.org/C2984157986","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Periodic orbits","level":2,"score":0.6012677550315857},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5443491339683533},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44524848461151123},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.43515995144844055},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4239363372325897},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.35814741253852844},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22284460067749023},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19821399450302124},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1395111382007599},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s10208-017-9369-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-017-9369-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-017-9369-5.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"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":"Foundations of Computational Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1607.01080","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1607.01080","pdf_url":"https://arxiv.org/pdf/1607.01080","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:ruj.uj.edu.pl:item/62636","is_oa":true,"landing_page_url":"https://ruj.uj.edu.pl/xmlui/handle/item/62636","pdf_url":"http://ruj.uj.edu.pl/bitstreams/cbcc5daa-3fc6-44ef-bbe9-67d471d4f250/download","source":{"id":"https://openalex.org/S4306401249","display_name":"Jagiellonian University Repository (Jagiellonian University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I126596746","host_organization_name":"Jagiellonian University","host_organization_lineage":["https://openalex.org/I126596746"],"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":"mag:2472428923","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1607.01080.pdf","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1607.01080","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1607.01080","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1007/s10208-017-9369-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-017-9369-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-017-9369-5.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"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":"Foundations of Computational Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2472428923.pdf","grobid_xml":"https://content.openalex.org/works/W2472428923.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W831210015","https://openalex.org/W1667530050","https://openalex.org/W1964053068","https://openalex.org/W1964354758","https://openalex.org/W1967216996","https://openalex.org/W1967490525","https://openalex.org/W1967778555","https://openalex.org/W1988090576","https://openalex.org/W1988906184","https://openalex.org/W1994376573","https://openalex.org/W2003645160","https://openalex.org/W2019704618","https://openalex.org/W2037957235","https://openalex.org/W2045256358","https://openalex.org/W2059276961","https://openalex.org/W2060064175","https://openalex.org/W2060579120","https://openalex.org/W2086576641","https://openalex.org/W2090082232","https://openalex.org/W2094631910","https://openalex.org/W2100375085","https://openalex.org/W2121020818","https://openalex.org/W2207050309","https://openalex.org/W2556753600","https://openalex.org/W2596696916","https://openalex.org/W2949565739","https://openalex.org/W3182252275","https://openalex.org/W4206215385","https://openalex.org/W4213080596","https://openalex.org/W4254705978"],"related_works":["https://openalex.org/W2396366554","https://openalex.org/W2024862670","https://openalex.org/W2008866301","https://openalex.org/W2300402141","https://openalex.org/W2150148181","https://openalex.org/W3209614745","https://openalex.org/W2562682806","https://openalex.org/W91083743","https://openalex.org/W2358960294","https://openalex.org/W1978196391","https://openalex.org/W2976902408","https://openalex.org/W2066458571","https://openalex.org/W2601212323","https://openalex.org/W2020034584","https://openalex.org/W1986793011","https://openalex.org/W2376921437","https://openalex.org/W2046289610","https://openalex.org/W2076194739","https://openalex.org/W1198038639","https://openalex.org/W3104481156"],"abstract_inverted_index":{"We":[0],"present":[1],"an":[2,20],"algorithm":[3],"for":[4],"the":[5,14,28,38,43],"rigorous":[6],"integration":[7],"of":[8,13,27,30],"delay":[9],"differential":[10],"equations":[11],"(DDEs)":[12],"form":[15],"$$x'(t)=f(x(t-\\tau":[16],"),x(t))$$":[17],".":[18],"As":[19],"application,":[21],"we":[22],"give":[23],"a":[24],"computer-assisted":[25],"proof":[26],"existence":[29],"two":[31],"attracting":[32],"periodic":[33],"orbits":[34],"(before":[35],"and":[36],"after":[37],"first":[39],"period-doubling":[40],"bifurcation)":[41],"in":[42],"Mackey\u2013Glass":[44],"equation.":[45]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2026-08-29T07:29:34.045763","created_date":"2025-10-10T00:00:00"}
