{"id":"https://openalex.org/W2066404061","doi":"https://doi.org/10.1137/070703028","title":"TC-HAT ($\\widehat{TC}$): A Novel Toolbox for the Continuation of Periodic Trajectories in Hybrid Dynamical Systems","display_name":"TC-HAT ($\\widehat{TC}$): A Novel Toolbox for the Continuation of Periodic Trajectories in Hybrid Dynamical Systems","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2066404061","doi":"https://doi.org/10.1137/070703028","mag":"2066404061"},"language":"en","primary_location":{"id":"doi:10.1137/070703028","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070703028","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},"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/A5004606598","display_name":"Phanikrishna Thota","orcid":null},"institutions":[{"id":"https://openalex.org/I36234482","display_name":"University of Bristol","ror":"https://ror.org/0524sp257","country_code":"GB","type":"education","lineage":["https://openalex.org/I36234482"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Phanikrishna Thota","raw_affiliation_strings":["University of Bristol"],"affiliations":[{"raw_affiliation_string":"University of Bristol","institution_ids":["https://openalex.org/I36234482"]}]},{"author_position":"last","author":{"id":null,"display_name":"Harry Dankowicz","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Harry Dankowicz","raw_affiliation_strings":["Information Trust Institute"],"affiliations":[{"raw_affiliation_string":"Information Trust Institute","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5004606598"],"corresponding_institution_ids":["https://openalex.org/I36234482"],"apc_list":null,"apc_paid":null,"fwci":11.8331,"has_fulltext":false,"cited_by_count":95,"citation_normalized_percentile":{"value":0.98781597,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"7","issue":"4","first_page":"1283","last_page":"1322"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11372","display_name":"Hydraulic and Pneumatic Systems","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/T11372","display_name":"Hydraulic and Pneumatic Systems","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/T11394","display_name":"Dynamics and Control of Mechanical Systems","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T13286","display_name":"Modeling and Simulation Systems","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.7373104095458984},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.6859237551689148},{"id":"https://openalex.org/keywords/continuation","display_name":"Continuation","score":0.6564059853553772},{"id":"https://openalex.org/keywords/hybrid-system","display_name":"Hybrid system","score":0.6012794375419617},{"id":"https://openalex.org/keywords/toolbox","display_name":"Toolbox","score":0.5373389720916748},{"id":"https://openalex.org/keywords/codimension","display_name":"Codimension","score":0.5100458264350891},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.49056023359298706},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47067055106163025},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4541085362434387},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.43417054414749146},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.42843306064605713},{"id":"https://openalex.org/keywords/periodic-boundary-conditions","display_name":"Periodic boundary conditions","score":0.41880345344543457},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37064218521118164},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3372856080532074},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.2952839136123657},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23097887635231018},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.11913323402404785}],"concepts":[{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.7373104095458984},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.6859237551689148},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.6564059853553772},{"id":"https://openalex.org/C50897621","wikidata":"https://www.wikidata.org/wiki/Q2665508","display_name":"Hybrid system","level":2,"score":0.6012794375419617},{"id":"https://openalex.org/C2777655017","wikidata":"https://www.wikidata.org/wiki/Q1501161","display_name":"Toolbox","level":2,"score":0.5373389720916748},{"id":"https://openalex.org/C83979697","wikidata":"https://www.wikidata.org/wiki/Q1778247","display_name":"Codimension","level":2,"score":0.5100458264350891},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.49056023359298706},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47067055106163025},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4541085362434387},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.43417054414749146},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.42843306064605713},{"id":"https://openalex.org/C112675119","wikidata":"https://www.wikidata.org/wiki/Q2992284","display_name":"Periodic boundary conditions","level":3,"score":0.41880345344543457},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37064218521118164},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3372856080532074},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.2952839136123657},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23097887635231018},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.11913323402404785},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/070703028","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070703028","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":54,"referenced_works":["https://openalex.org/W1516289514","https://openalex.org/W1519503234","https://openalex.org/W1526187193","https://openalex.org/W1560787783","https://openalex.org/W1605155529","https://openalex.org/W1606901107","https://openalex.org/W1965778005","https://openalex.org/W1973112162","https://openalex.org/W1983736546","https://openalex.org/W1991739136","https://openalex.org/W1995449663","https://openalex.org/W1999832239","https://openalex.org/W2000068191","https://openalex.org/W2002247803","https://openalex.org/W2002403383","https://openalex.org/W2002895823","https://openalex.org/W2005988040","https://openalex.org/W2007053845","https://openalex.org/W2011033548","https://openalex.org/W2013456332","https://openalex.org/W2014898529","https://openalex.org/W2015898169","https://openalex.org/W2017343026","https://openalex.org/W2027333056","https://openalex.org/W2028047871","https://openalex.org/W2033706714","https://openalex.org/W2046046830","https://openalex.org/W2048017269","https://openalex.org/W2057307649","https://openalex.org/W2059380896","https://openalex.org/W2059498062","https://openalex.org/W2065773966","https://openalex.org/W2073555305","https://openalex.org/W2073686912","https://openalex.org/W2076273493","https://openalex.org/W2077549689","https://openalex.org/W2081696580","https://openalex.org/W2088986191","https://openalex.org/W2090022960","https://openalex.org/W2091314510","https://openalex.org/W2091534537","https://openalex.org/W2091931106","https://openalex.org/W2116098329","https://openalex.org/W2126076281","https://openalex.org/W2130366329","https://openalex.org/W2138750465","https://openalex.org/W2144249884","https://openalex.org/W2155615510","https://openalex.org/W2158552064","https://openalex.org/W2164761951","https://openalex.org/W2229701272","https://openalex.org/W2581487981","https://openalex.org/W2905382927","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2001261028","https://openalex.org/W59350782","https://openalex.org/W1201114281","https://openalex.org/W4296423504","https://openalex.org/W3088359067","https://openalex.org/W2150264438","https://openalex.org/W2127167559","https://openalex.org/W2079371292","https://openalex.org/W2066404061","https://openalex.org/W3139805742"],"abstract_inverted_index":{"This":[0],"paper":[1],"describes":[2],"the":[3,9,61,64],"underlying":[4],"formulation":[5],"and":[6,44,50],"functionality":[7],"of":[8,21,47,63,72],"newly":[10],"developed":[11],"software":[12],"program":[13,65],"$\\widehat{\\text{{\\sc":[14],"tc}}}$":[15],"(\u201ctc-hat\u201d),":[16],"to":[17,34,42],"perform":[18],"bifurcation":[19,70],"analysis":[20,71],"systems":[22,57],"in":[23,55],"which":[24],"continuous-in-time":[25],"dynamics":[26],"are":[27,58,66],"interrupted":[28],"by":[29,68],"discrete-in-time":[30],"events,":[31],"often":[32],"referred":[33],"as":[35],"hybrid":[36,76],"dynamical":[37,77],"systems.":[38,78],"Boundary-value-problem":[39],"formulations":[40],"corresponding":[41],"single-":[43],"two-parameter":[45],"continuations":[46],"periodic":[48],"trajectories":[49],"selected":[51],"associated":[52],"codimension-one":[53],"bifurcations":[54],"such":[56],"presented.":[59],"Finally,":[60],"capabilities":[62],"illustrated":[67],"performing":[69],"a":[73],"few":[74],"example":[75]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}