{"id":"https://openalex.org/W1969684856","doi":"https://doi.org/10.1007/s004220050501","title":"A mathematical criterion based on phase response curves for stability in a ring of coupled oscillators","display_name":"A mathematical criterion based on phase response curves for stability in a ring of coupled oscillators","publication_year":1999,"publication_date":"1999-01-07","ids":{"openalex":"https://openalex.org/W1969684856","doi":"https://doi.org/10.1007/s004220050501","mag":"1969684856","pmid":"https://pubmed.ncbi.nlm.nih.gov/20809292"},"language":"en","primary_location":{"id":"doi:10.1007/s004220050501","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s004220050501","pdf_url":null,"source":{"id":"https://openalex.org/S87357125","display_name":"Biological Cybernetics","issn_l":"0340-1200","issn":["0340-1200","1432-0770"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Biological Cybernetics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061322136","display_name":"Ron O. Dror","orcid":"https://orcid.org/0000-0002-6418-2793"},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"R. O. Dror","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Rice University, Houston, TX 77005-1892, USA, , , , , , US","Department of Electrical and Computer Engineering, Rice University, Houston, TX 77005-1892, USA, US"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Rice University, Houston, TX 77005-1892, USA, , , , , , US","institution_ids":["https://openalex.org/I74775410"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Rice University, Houston, TX 77005-1892, USA, US","institution_ids":["https://openalex.org/I74775410"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056283225","display_name":"Carmen C. Canavier","orcid":"https://orcid.org/0000-0003-4368-6906"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"C. C. Canavier","raw_affiliation_strings":["Department of Neurobiology and Anatomy, University of Texas Medical School, PO Box 20708, Houston, Texas 77225, USA, , , , , , US","Department of Neurobiology and Anatomy, University of Texas Medical School, PO Box 20708, Houston, Texas 77225, USA, US"],"affiliations":[{"raw_affiliation_string":"Department of Neurobiology and Anatomy, University of Texas Medical School, PO Box 20708, Houston, Texas 77225, USA, , , , , , US","institution_ids":["https://openalex.org/I86519309"]},{"raw_affiliation_string":"Department of Neurobiology and Anatomy, University of Texas Medical School, PO Box 20708, Houston, Texas 77225, USA, US","institution_ids":["https://openalex.org/I86519309"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085073238","display_name":"Robert J. Butera","orcid":"https://orcid.org/0000-0002-1806-0621"},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"R. J. Butera","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Rice University, Houston, TX 77005-1892, USA, , , , , , US","Department of Electrical and Computer Engineering, Rice University, Houston, TX 77005-1892, USA, US"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Rice University, Houston, TX 77005-1892, USA, , , , , , US","institution_ids":["https://openalex.org/I74775410"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Rice University, Houston, TX 77005-1892, USA, US","institution_ids":["https://openalex.org/I74775410"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113972802","display_name":"John W. Clark","orcid":null},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. W. Clark","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Rice University, Houston, TX 77005-1892, USA, , , , , , US","Department of Electrical and Computer Engineering, Rice University, Houston, TX 77005-1892, USA, US"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Rice University, Houston, TX 77005-1892, USA, , , , , , US","institution_ids":["https://openalex.org/I74775410"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Rice University, Houston, TX 77005-1892, USA, US","institution_ids":["https://openalex.org/I74775410"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084117702","display_name":"John H. Byrne","orcid":"https://orcid.org/0000-0001-7947-5890"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. H. Byrne","raw_affiliation_strings":["Department of Neurobiology and Anatomy, University of Texas Medical School, PO Box 20708, Houston, Texas 77225, USA, , , , , , US","Department of Neurobiology and Anatomy, University of Texas Medical School, PO Box 20708, Houston, Texas 77225, USA, US"],"affiliations":[{"raw_affiliation_string":"Department of Neurobiology and Anatomy, University of Texas Medical School, PO Box 20708, Houston, Texas 77225, USA, , , , , , US","institution_ids":["https://openalex.org/I86519309"]},{"raw_affiliation_string":"Department of Neurobiology and Anatomy, University of Texas Medical School, PO Box 20708, Houston, Texas 77225, USA, US","institution_ids":["https://openalex.org/I86519309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5061322136"],"corresponding_institution_ids":["https://openalex.org/I74775410"],"apc_list":{"value":2790,"currency":"EUR","value_usd":3590},"apc_paid":null,"fwci":1.4822,"has_fulltext":false,"cited_by_count":82,"citation_normalized_percentile":{"value":0.80538347,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"80","issue":"1","first_page":"11","last_page":"23"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11601","display_name":"Neuroscience and Neural Engineering","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/2804","display_name":"Cellular and Molecular Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.6445452570915222},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.6130306720733643},{"id":"https://openalex.org/keywords/stability-criterion","display_name":"Stability criterion","score":0.5717647075653076},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5561392307281494},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.543026328086853},{"id":"https://openalex.org/keywords/entrainment","display_name":"Entrainment (biomusicology)","score":0.4905046820640564},{"id":"https://openalex.org/keywords/phase-response-curve","display_name":"Phase response curve","score":0.4771817922592163},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.434447705745697},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3801012337207794},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.32066527009010315},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22277411818504333},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1161070168018341},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08454740047454834},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.07667002081871033}],"concepts":[{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6445452570915222},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.6130306720733643},{"id":"https://openalex.org/C2778925954","wikidata":"https://www.wikidata.org/wiki/Q16883749","display_name":"Stability criterion","level":3,"score":0.5717647075653076},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5561392307281494},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.543026328086853},{"id":"https://openalex.org/C139992725","wikidata":"https://www.wikidata.org/wiki/Q5380656","display_name":"Entrainment (biomusicology)","level":3,"score":0.4905046820640564},{"id":"https://openalex.org/C63531555","wikidata":"https://www.wikidata.org/wiki/Q7180960","display_name":"Phase response curve","level":4,"score":0.4771817922592163},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.434447705745697},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3801012337207794},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.32066527009010315},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22277411818504333},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1161070168018341},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08454740047454834},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.07667002081871033},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C135343436","wikidata":"https://www.wikidata.org/wiki/Q170406","display_name":"Rhythm","level":2,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C38606739","wikidata":"https://www.wikidata.org/wiki/Q5121352","display_name":"Circadian clock","level":3,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s004220050501","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s004220050501","pdf_url":null,"source":{"id":"https://openalex.org/S87357125","display_name":"Biological Cybernetics","issn_l":"0340-1200","issn":["0340-1200","1432-0770"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Biological Cybernetics","raw_type":"journal-article"},{"id":"pmid:20809292","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/20809292","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Biological cybernetics","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W38670037","https://openalex.org/W81727061","https://openalex.org/W1488708381","https://openalex.org/W1544532551","https://openalex.org/W1654369324","https://openalex.org/W1972998826","https://openalex.org/W1973971566","https://openalex.org/W1980788971","https://openalex.org/W1988551154","https://openalex.org/W1991835281","https://openalex.org/W1992076880","https://openalex.org/W2006926036","https://openalex.org/W2008562163","https://openalex.org/W2011722983","https://openalex.org/W2034014645","https://openalex.org/W2075674413","https://openalex.org/W2079133700","https://openalex.org/W2083535648","https://openalex.org/W2088678566","https://openalex.org/W2089876099","https://openalex.org/W2094058963","https://openalex.org/W2100649861","https://openalex.org/W2125444472","https://openalex.org/W2323515175","https://openalex.org/W3027010045","https://openalex.org/W3195872149"],"related_works":["https://openalex.org/W3206121223","https://openalex.org/W2055318650","https://openalex.org/W1994766193","https://openalex.org/W4310634407","https://openalex.org/W2053379810","https://openalex.org/W2076613424","https://openalex.org/W2016129950","https://openalex.org/W1983106629","https://openalex.org/W2175177745","https://openalex.org/W1998230106"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":5}],"updated_date":"2026-01-13T01:12:25.745995","created_date":"2025-10-10T00:00:00"}
