{"id":"https://openalex.org/W2083694019","doi":"https://doi.org/10.1007/bf02429870","title":"Coupled nonlinear oscillators and the symmetries of animal gaits","display_name":"Coupled nonlinear oscillators and the symmetries of animal gaits","publication_year":1993,"publication_date":"1993-12-01","ids":{"openalex":"https://openalex.org/W2083694019","doi":"https://doi.org/10.1007/bf02429870","mag":"2083694019"},"language":"en","primary_location":{"id":"doi:10.1007/bf02429870","doi":"https://doi.org/10.1007/bf02429870","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02429870","pdf_url":null,"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,"listed_in":["cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-1"],"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":"Journal of Nonlinear Science","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"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/A5065209470","display_name":"James J. Collins","orcid":"https://orcid.org/0000-0002-5560-8246","observed_orcids":["https://orcid.org/0000-0002-5560-8246"]},"institutions":[{"id":"https://openalex.org/I111088046","display_name":"Boston University","ror":"https://ror.org/05qwgg493","country_code":"US","type":"education","lineage":["https://openalex.org/I111088046"]},{"id":"https://openalex.org/I2801809904","display_name":"Nuffield Orthopaedic Centre","ror":"https://ror.org/0036ate90","country_code":"GB","type":"healthcare","lineage":["https://openalex.org/I2801809904","https://openalex.org/I4210147381"]},{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"J. J. Collins","raw_affiliation_strings":["NeuroMuscular Research Center and Department of Biomedical Engineering, Boston University, 02215, Boston, MA, USA","Oxford Orthopaedic Engineering Centre, Nuffield Orthopaedic Centre, University of Oxford, OX3 7LD, Headington, Oxford, UK","NeuroMuscular Research Center and Department of Biomedical Engineering, Boston University, Boston, USA","Oxford Orthopaedic Engineering Centre, Nuffield Orthopaedic Centre, University of Oxford, Headington, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"NeuroMuscular Research Center and Department of Biomedical Engineering, Boston University, 02215, Boston, MA, USA","institution_ids":["https://openalex.org/I111088046"]},{"raw_affiliation_string":"Oxford Orthopaedic Engineering Centre, Nuffield Orthopaedic Centre, University of Oxford, OX3 7LD, Headington, Oxford, UK","institution_ids":["https://openalex.org/I2801809904","https://openalex.org/I40120149"]},{"raw_affiliation_string":"NeuroMuscular Research Center and Department of Biomedical Engineering, Boston University, Boston, USA","institution_ids":["https://openalex.org/I111088046"]},{"raw_affiliation_string":"Oxford Orthopaedic Engineering Centre, Nuffield Orthopaedic Centre, University of Oxford, Headington, UK","institution_ids":["https://openalex.org/I2801809904","https://openalex.org/I40120149"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079169390","display_name":"Ian Nicholas Stewart","orcid":"https://orcid.org/0000-0002-3759-0142","observed_orcids":["https://orcid.org/0000-0002-3759-0142"]},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"I. N. Stewart","raw_affiliation_strings":["Nonlinear Systems Laboratory, Mathematics Institute, University of Warwick, CV4 7AL, Coventry, UK","Nonlinear Systems Laboratory, Mathematics Institute, University of Warwick, Coventry, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nonlinear Systems Laboratory, Mathematics Institute, University of Warwick, CV4 7AL, Coventry, UK","institution_ids":["https://openalex.org/I39555362"]},{"raw_affiliation_string":"Nonlinear Systems Laboratory, Mathematics Institute, University of Warwick, Coventry, UK","institution_ids":["https://openalex.org/I39555362"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3290,"currency":"USD","value_usd":3290},"apc_paid":null,"fwci":11.646,"has_fulltext":false,"cited_by_count":499,"citation_normalized_percentile":{"value":0.9941543,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"3","issue":"1","first_page":"349","last_page":"392"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10879","display_name":"Robotic Locomotion and Control","score":0.9003999829292297,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10879","display_name":"Robotic Locomotion and Control","score":0.9003999829292297,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.09399999678134918,"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"}},{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.0010999999940395355,"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/coupled-nonlinear-oscillators","display_name":"coupled nonlinear oscillators","score":0.9110000133514404},{"id":"https://openalex.org/keywords/gait-symmetry","display_name":"gait symmetry","score":0.8029999732971191},{"id":"https://openalex.org/keywords/central-pattern-generator","display_name":"central pattern generator","score":0.9210000038146973},{"id":"https://openalex.org/keywords/symmetry-breaking-bifurcation","display_name":"symmetry-breaking bifurcation","score":0.9380000233650208},{"id":"https://openalex.org/keywords/oscillator-networks","display_name":"oscillator networks","score":0.8080000281333923},{"id":"https://openalex.org/keywords/gait-transition","display_name":"gait transition","score":0.9750000238418579}],"concepts":[{"id":"https://openalex.org/C151800584","wikidata":"https://www.wikidata.org/wiki/Q2370000","display_name":"Gait","level":2,"score":0.7158755660057068},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.665751039981842},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.6160287261009216},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5827268958091736},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43758103251457214},{"id":"https://openalex.org/C204795200","wikidata":"https://www.wikidata.org/wiki/Q903282","display_name":"Symmetry breaking","level":2,"score":0.4275549650192261},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4066951274871826},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36863672733306885},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.36027848720550537},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.31313377618789673},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.20782777667045593},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15118619799613953},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.14483198523521423},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C42407357","wikidata":"https://www.wikidata.org/wiki/Q521","display_name":"Physiology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/bf02429870","doi":"https://doi.org/10.1007/bf02429870","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02429870","pdf_url":null,"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,"listed_in":["cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-1"],"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":"Journal of Nonlinear Science","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.547.9671","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.547.9671","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.bu.edu/abl/files/jnonlinearsci_collins.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":58,"referenced_works":["https://openalex.org/W102106719","https://openalex.org/W130863730","https://openalex.org/W170508163","https://openalex.org/W245229885","https://openalex.org/W307773229","https://openalex.org/W365407947","https://openalex.org/W612028068","https://openalex.org/W1480343083","https://openalex.org/W1492295676","https://openalex.org/W1534857865","https://openalex.org/W1595224832","https://openalex.org/W1896323103","https://openalex.org/W1963656947","https://openalex.org/W1965778005","https://openalex.org/W1966084770","https://openalex.org/W1977264099","https://openalex.org/W1979241164","https://openalex.org/W1980788971","https://openalex.org/W1982508615","https://openalex.org/W1986254472","https://openalex.org/W1986401459","https://openalex.org/W1988685143","https://openalex.org/W1990028683","https://openalex.org/W1990723956","https://openalex.org/W1991593435","https://openalex.org/W1995682655","https://openalex.org/W1997576152","https://openalex.org/W2002101416","https://openalex.org/W2003999060","https://openalex.org/W2006276798","https://openalex.org/W2006821796","https://openalex.org/W2008562163","https://openalex.org/W2021973929","https://openalex.org/W2030086547","https://openalex.org/W2042977650","https://openalex.org/W2055236981","https://openalex.org/W2060271150","https://openalex.org/W2064607447","https://openalex.org/W2066751804","https://openalex.org/W2069032592","https://openalex.org/W2078794407","https://openalex.org/W2089359955","https://openalex.org/W2090074774","https://openalex.org/W2090235705","https://openalex.org/W2090373601","https://openalex.org/W2092446028","https://openalex.org/W2093485175","https://openalex.org/W2094770975","https://openalex.org/W2099600411","https://openalex.org/W2100649861","https://openalex.org/W2145932718","https://openalex.org/W2153624629","https://openalex.org/W2155732403","https://openalex.org/W2159240874","https://openalex.org/W2172735470","https://openalex.org/W2316793170","https://openalex.org/W3022035939","https://openalex.org/W4255777804"],"related_works":["https://openalex.org/W7221128293","https://openalex.org/W7096099851","https://openalex.org/W1990723956","https://openalex.org/W2065257125","https://openalex.org/W2785896536","https://openalex.org/W2091086093","https://openalex.org/W4394648572","https://openalex.org/W2098581246","https://openalex.org/W173244898","https://openalex.org/W7101211045"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":12},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":15},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":13},{"year":2018,"cited_by_count":15},{"year":2017,"cited_by_count":18},{"year":2016,"cited_by_count":19},{"year":2015,"cited_by_count":18},{"year":2014,"cited_by_count":11},{"year":2013,"cited_by_count":28},{"year":2012,"cited_by_count":9}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}