{"id":"https://openalex.org/W2754812564","doi":"https://doi.org/10.1155/2017/2796090","title":"Nonlinear Dynamics of a PI Hydroturbine Governing System with Double Delays","display_name":"Nonlinear Dynamics of a PI Hydroturbine Governing System with Double Delays","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2754812564","doi":"https://doi.org/10.1155/2017/2796090","mag":"2754812564"},"language":"en","primary_location":{"id":"doi:10.1155/2017/2796090","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2017/2796090","pdf_url":"http://downloads.hindawi.com/journals/jcse/2017/2796090.pdf","source":{"id":"https://openalex.org/S11704996","display_name":"Journal of Control Science and Engineering","issn_l":"1687-5249","issn":["1687-5249","1687-5257"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Control Science and Engineering","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"http://downloads.hindawi.com/journals/jcse/2017/2796090.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101448012","display_name":"Hongwei Luo","orcid":"https://orcid.org/0000-0002-0310-1590"},"institutions":[{"id":"https://openalex.org/I4210124553","display_name":"Gansu Research Academy of Forestry Science and Technology","ror":"https://ror.org/02rsv1244","country_code":"CN","type":"other","lineage":["https://openalex.org/I4210124553"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongwei Luo","raw_affiliation_strings":["School of Information Engineering, Gansu Forestry Technological College, Tianshui, Gansu 741020, China"],"raw_orcid":"https://orcid.org/0000-0002-0310-1590","affiliations":[{"raw_affiliation_string":"School of Information Engineering, Gansu Forestry Technological College, Tianshui, Gansu 741020, China","institution_ids":["https://openalex.org/I4210124553"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053730220","display_name":"Jiangang Zhang","orcid":"https://orcid.org/0000-0002-8523-6623"},"institutions":[{"id":"https://openalex.org/I3133134087","display_name":"Lanzhou Jiaotong University","ror":"https://ror.org/03144pv92","country_code":"CN","type":"education","lineage":["https://openalex.org/I3133134087"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jiangang Zhang","raw_affiliation_strings":["School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, China"],"raw_orcid":"https://orcid.org/0000-0002-8523-6623","affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, China","institution_ids":["https://openalex.org/I3133134087"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057739616","display_name":"Wenju Du","orcid":null},"institutions":[{"id":"https://openalex.org/I3133134087","display_name":"Lanzhou Jiaotong University","ror":"https://ror.org/03144pv92","country_code":"CN","type":"education","lineage":["https://openalex.org/I3133134087"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenju Du","raw_affiliation_strings":["School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, China"],"raw_orcid":"https://orcid.org/0000-0002-9862-4924","affiliations":[{"raw_affiliation_string":"School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, China","institution_ids":["https://openalex.org/I3133134087"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109711517","display_name":"Jiarong Lu","orcid":"https://orcid.org/0000-0001-5846-4412"},"institutions":[{"id":"https://openalex.org/I94047373","display_name":"Xinjiang University of Finance and Economics","ror":"https://ror.org/00fk31757","country_code":"CN","type":"education","lineage":["https://openalex.org/I94047373"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiarong Lu","raw_affiliation_strings":["School of Applied Mathematics, Xinjiang University of Finance & Economics, Wulumuqi, Xinjiang 830000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Applied Mathematics, Xinjiang University of Finance & Economics, Wulumuqi, Xinjiang 830000, China","institution_ids":["https://openalex.org/I94047373"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035525276","display_name":"Xinlei An","orcid":"https://orcid.org/0000-0003-2424-4870"},"institutions":[{"id":"https://openalex.org/I3133134087","display_name":"Lanzhou Jiaotong University","ror":"https://ror.org/03144pv92","country_code":"CN","type":"education","lineage":["https://openalex.org/I3133134087"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xinlei An","raw_affiliation_strings":["School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, China","institution_ids":["https://openalex.org/I3133134087"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5053730220"],"corresponding_institution_ids":["https://openalex.org/I3133134087"],"apc_list":{"value":1400,"currency":"USD","value_usd":1400},"apc_paid":{"value":1400,"currency":"USD","value_usd":1400},"fwci":0.2485,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.66936318,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"2017","issue":null,"first_page":"1","last_page":"14"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9944999814033508,"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"}},"topics":[{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9944999814033508,"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"}},{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9909999966621399,"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/T10244","display_name":"Chaos control and synchronization","score":0.9868000149726868,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.8021754026412964},{"id":"https://openalex.org/keywords/center-manifold","display_name":"Center manifold","score":0.7606232166290283},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6051310896873474},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5929651856422424},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5609952211380005},{"id":"https://openalex.org/keywords/pitchfork-bifurcation","display_name":"Pitchfork bifurcation","score":0.5231370329856873},{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.49468299746513367},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.49119970202445984},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.48567450046539307},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.4614388644695282},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4441887438297272},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.44193077087402344},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3503686487674713},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19059965014457703},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15266451239585876}],"concepts":[{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.8021754026412964},{"id":"https://openalex.org/C74774103","wikidata":"https://www.wikidata.org/wiki/Q4504202","display_name":"Center manifold","level":5,"score":0.7606232166290283},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6051310896873474},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5929651856422424},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5609952211380005},{"id":"https://openalex.org/C155092403","wikidata":"https://www.wikidata.org/wiki/Q1785924","display_name":"Pitchfork bifurcation","level":5,"score":0.5231370329856873},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.49468299746513367},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.49119970202445984},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.48567450046539307},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.4614388644695282},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4441887438297272},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.44193077087402344},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3503686487674713},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19059965014457703},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15266451239585876},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","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":2,"locations":[{"id":"doi:10.1155/2017/2796090","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2017/2796090","pdf_url":"http://downloads.hindawi.com/journals/jcse/2017/2796090.pdf","source":{"id":"https://openalex.org/S11704996","display_name":"Journal of Control Science and Engineering","issn_l":"1687-5249","issn":["1687-5249","1687-5257"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Control Science and Engineering","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:acb85e2a4f074eb48ff358fa2a5ae197","is_oa":true,"landing_page_url":"https://doaj.org/article/acb85e2a4f074eb48ff358fa2a5ae197","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Control Science and Engineering, Vol 2017 (2017)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2017/2796090","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2017/2796090","pdf_url":"http://downloads.hindawi.com/journals/jcse/2017/2796090.pdf","source":{"id":"https://openalex.org/S11704996","display_name":"Journal of Control Science and Engineering","issn_l":"1687-5249","issn":["1687-5249","1687-5257"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Control Science and Engineering","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.7300000190734863}],"awards":[{"id":"https://openalex.org/G2108334440","display_name":null,"funder_award_id":"2015-RC-3","funder_id":"https://openalex.org/F4320329850","funder_display_name":"Innovation and Entrepreneurship Talent Project of Lanzhou"},{"id":"https://openalex.org/G3093680703","display_name":null,"funder_award_id":"61364001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8208320846","display_name":null,"funder_award_id":"2015-RC-3","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320329850","display_name":"Innovation and Entrepreneurship Talent Project of Lanzhou","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2754812564.pdf","grobid_xml":"https://content.openalex.org/works/W2754812564.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1988881797","https://openalex.org/W1989892089","https://openalex.org/W1997628743","https://openalex.org/W1997817337","https://openalex.org/W2005496030","https://openalex.org/W2010026351","https://openalex.org/W2014509488","https://openalex.org/W2015534115","https://openalex.org/W2017845303","https://openalex.org/W2020506869","https://openalex.org/W2028437524","https://openalex.org/W2029574848","https://openalex.org/W2030570384","https://openalex.org/W2031368558","https://openalex.org/W2053780452","https://openalex.org/W2054019601","https://openalex.org/W2068800853","https://openalex.org/W2078372393","https://openalex.org/W2084827931","https://openalex.org/W2084834371","https://openalex.org/W2113223222","https://openalex.org/W2124843179","https://openalex.org/W2148476832","https://openalex.org/W2148520776","https://openalex.org/W2177349431","https://openalex.org/W2466416774","https://openalex.org/W2554930615","https://openalex.org/W4253601996"],"related_works":["https://openalex.org/W2546487931","https://openalex.org/W2024878967","https://openalex.org/W56905705","https://openalex.org/W3042510364","https://openalex.org/W2356715721","https://openalex.org/W4379507489","https://openalex.org/W2352502327","https://openalex.org/W2385123893","https://openalex.org/W2737309493","https://openalex.org/W2884051366"],"abstract_inverted_index":{"A":[0],"PI":[1,37],"hydroturbine":[2,38],"governing":[3,39],"system":[4,21,40,58,117],"with":[5,41],"saturation":[6],"and":[7,32,52,71,86,96,120],"double":[8,42],"delays":[9,43],"is":[10,22],"generated":[11],"in":[12],"small":[13],"perturbation.":[14],"The":[15,107],"nonlinear":[16],"dynamic":[17],"behavior":[18],"of":[19,35,56,68,74,98,124,139],"the":[20,30,36,45,57,66,72,75,82,94,99,115,122,125,137,140],"investigated.":[23],"More":[24],"precisely,":[25],"at":[26,61],"first,":[27],"we":[28],"analyze":[29],"stability":[31,50,67,95,119,123],"Hopf":[33,53,76,100],"bifurcation":[34,54,77,101],"under":[44],"four":[46],"different":[47],"cases.":[48],"Corresponding":[49],"theorem":[51,55],"are":[59,78,102,133],"obtained":[60],"equilibrium":[62],"points.":[63],"And":[64],"then":[65],"periodic":[69],"solution":[70],"direction":[73,97],"illustrated":[79],"by":[80,104],"using":[81],"normal":[83],"form":[84],"method":[85],"center":[87],"manifold":[88],"theorem.":[89],"We":[90],"find":[91],"out":[92],"that":[93],"determined":[103],"three":[105],"parameters.":[106],"results":[108],"have":[109],"great":[110],"realistic":[111],"significance":[112],"to":[113,135],"guarantee":[114],"power":[116],"frequency":[118],"improve":[121],"hydropower":[126],"system.":[127],"At":[128],"last,":[129],"some":[130],"numerical":[131],"examples":[132],"given":[134],"verify":[136],"correctness":[138],"theoretical":[141],"results.":[142]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}