{"id":"https://openalex.org/W2170939660","doi":"https://doi.org/10.1109/ijcnn.2007.4370977","title":"Complex-valued Neuron to describe the Dynamics after Hopf Bifurcation: an Example of CPG Model for a Biped Locomotion","display_name":"Complex-valued Neuron to describe the Dynamics after Hopf Bifurcation: an Example of CPG Model for a Biped Locomotion","publication_year":2007,"publication_date":"2007-08-01","ids":{"openalex":"https://openalex.org/W2170939660","doi":"https://doi.org/10.1109/ijcnn.2007.4370977","mag":"2170939660"},"language":"en","primary_location":{"id":"doi:10.1109/ijcnn.2007.4370977","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ijcnn.2007.4370977","pdf_url":null,"source":{"id":"https://openalex.org/S4210195743","display_name":"IEEE International Conference on Neural Networks/IEEE ... International Conference on Neural Networks","issn_l":"1098-7576","issn":["1098-7576","1558-3902"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 International Joint Conference on Neural Networks","raw_type":"proceedings-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/A5078994792","display_name":"Ikuko Nishikawa","orcid":"https://orcid.org/0000-0003-4780-0155"},"institutions":[{"id":"https://openalex.org/I135768898","display_name":"Ritsumeikan University","ror":"https://ror.org/0197nmd03","country_code":"JP","type":"education","lineage":["https://openalex.org/I135768898","https://openalex.org/I4390039241"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Ikuko Nishikawa","raw_affiliation_strings":["College of Information Science and Engineering, Ritsumeikan University, Kusatsu, Shiga, Japan"],"affiliations":[{"raw_affiliation_string":"College of Information Science and Engineering, Ritsumeikan University, Kusatsu, Shiga, Japan","institution_ids":["https://openalex.org/I135768898"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036534205","display_name":"Kohei Hayashi","orcid":"https://orcid.org/0000-0002-8758-8139"},"institutions":[{"id":"https://openalex.org/I135768898","display_name":"Ritsumeikan University","ror":"https://ror.org/0197nmd03","country_code":"JP","type":"education","lineage":["https://openalex.org/I135768898","https://openalex.org/I4390039241"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Kohei Hayashi","raw_affiliation_strings":["College of Information Science and Engineering, Ritsumeikan University, Kusatsu, Shiga, Japan"],"affiliations":[{"raw_affiliation_string":"College of Information Science and Engineering, Ritsumeikan University, Kusatsu, Shiga, Japan","institution_ids":["https://openalex.org/I135768898"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113386958","display_name":"Kazutoshi Sakakibara","orcid":"https://orcid.org/0009-0000-9786-8460"},"institutions":[{"id":"https://openalex.org/I135768898","display_name":"Ritsumeikan University","ror":"https://ror.org/0197nmd03","country_code":"JP","type":"education","lineage":["https://openalex.org/I135768898","https://openalex.org/I4390039241"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Kazutoshi Sakakibara","raw_affiliation_strings":["College of Information Science and Engineering, Ritsumeikan University, Kusatsu, Shiga, Japan"],"affiliations":[{"raw_affiliation_string":"College of Information Science and Engineering, Ritsumeikan University, Kusatsu, Shiga, Japan","institution_ids":["https://openalex.org/I135768898"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5078994792"],"corresponding_institution_ids":["https://openalex.org/I135768898"],"apc_list":null,"apc_paid":null,"fwci":0.3953,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.62390101,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"5","issue":null,"first_page":"327","last_page":"332"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9977999925613403,"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":0.9977999925613403,"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/T10581","display_name":"Neural dynamics and brain function","score":0.9973999857902527,"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":0.9958000183105469,"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/biological-applications-of-bifurcation-theory","display_name":"Biological applications of bifurcation theory","score":0.7536380887031555},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.730663537979126},{"id":"https://openalex.org/keywords/central-pattern-generator","display_name":"Central pattern generator","score":0.658323347568512},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.65630704164505},{"id":"https://openalex.org/keywords/synchronization","display_name":"Synchronization (alternating current)","score":0.6468217372894287},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.6388064622879028},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5862117409706116},{"id":"https://openalex.org/keywords/biological-neuron-model","display_name":"Biological neuron model","score":0.5593829154968262},{"id":"https://openalex.org/keywords/kuramoto-model","display_name":"Kuramoto model","score":0.4490714967250824},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.43354111909866333},{"id":"https://openalex.org/keywords/complex-dynamics","display_name":"Complex dynamics","score":0.43087196350097656},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.41174042224884033},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.39829400181770325},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38642627000808716},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.38150712847709656},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3671763241291046},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.32408350706100464},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.3037148714065552},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21020084619522095},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1321185827255249},{"id":"https://openalex.org/keywords/rhythm","display_name":"Rhythm","score":0.12332531809806824},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.0841664969921112}],"concepts":[{"id":"https://openalex.org/C174914120","wikidata":"https://www.wikidata.org/wiki/Q4914973","display_name":"Biological applications of bifurcation theory","level":5,"score":0.7536380887031555},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.730663537979126},{"id":"https://openalex.org/C169453685","wikidata":"https://www.wikidata.org/wiki/Q1054066","display_name":"Central pattern generator","level":3,"score":0.658323347568512},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.65630704164505},{"id":"https://openalex.org/C2778562939","wikidata":"https://www.wikidata.org/wiki/Q1298791","display_name":"Synchronization (alternating current)","level":3,"score":0.6468217372894287},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.6388064622879028},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5862117409706116},{"id":"https://openalex.org/C186565885","wikidata":"https://www.wikidata.org/wiki/Q1651163","display_name":"Biological neuron model","level":3,"score":0.5593829154968262},{"id":"https://openalex.org/C2780042749","wikidata":"https://www.wikidata.org/wiki/Q604374","display_name":"Kuramoto model","level":4,"score":0.4490714967250824},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.43354111909866333},{"id":"https://openalex.org/C126701199","wikidata":"https://www.wikidata.org/wiki/Q264224","display_name":"Complex dynamics","level":2,"score":0.43087196350097656},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.41174042224884033},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.39829400181770325},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38642627000808716},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.38150712847709656},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3671763241291046},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.32408350706100464},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.3037148714065552},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21020084619522095},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1321185827255249},{"id":"https://openalex.org/C135343436","wikidata":"https://www.wikidata.org/wiki/Q170406","display_name":"Rhythm","level":2,"score":0.12332531809806824},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0841664969921112},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"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/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/ijcnn.2007.4370977","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ijcnn.2007.4370977","pdf_url":null,"source":{"id":"https://openalex.org/S4210195743","display_name":"IEEE International Conference on Neural Networks/IEEE ... International Conference on Neural Networks","issn_l":"1098-7576","issn":["1098-7576","1558-3902"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 International Joint Conference on Neural Networks","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.6700000166893005}],"awards":[],"funders":[{"id":"https://openalex.org/F4320323289","display_name":"Ritsumeikan University","ror":"https://ror.org/0197nmd03"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W93167102","https://openalex.org/W111157985","https://openalex.org/W1543056723","https://openalex.org/W1550596064","https://openalex.org/W1993874474","https://openalex.org/W2043388563","https://openalex.org/W2047515252","https://openalex.org/W2089876099","https://openalex.org/W2109851675","https://openalex.org/W2169563904","https://openalex.org/W4236956886","https://openalex.org/W6603755213","https://openalex.org/W6676392675"],"related_works":["https://openalex.org/W2070766239","https://openalex.org/W4200143501","https://openalex.org/W2531139253","https://openalex.org/W2170939660","https://openalex.org/W2041466059","https://openalex.org/W2790543749","https://openalex.org/W2545601837","https://openalex.org/W2116185617","https://openalex.org/W2142228622","https://openalex.org/W3185700580"],"abstract_inverted_index":{"Complex-valued":[0],"Hopfield":[1],"network":[2,11,29,39],"is":[3,44,59],"used":[4,45],"to":[5,23],"model":[6,51],"the":[7,25,28,70,114,120,124,128,134],"dynamics":[8,30],"of":[9,12,17,27,40,93,104,113,123,127,137,141],"a":[10,32,38,47,53,60,138],"limit":[13],"cycle":[14],"oscillators,":[15],"each":[16],"which":[18,77,87],"emerges":[19],"via":[20],"Hopf":[21],"bifurcation,":[22],"investigate":[24],"dependency":[26],"on":[31],"bifurcation":[33,57],"parameter.":[34],"As":[35],"an":[36],"application,":[37],"two":[41],"complex-valued":[42,129],"neurons":[43],"as":[46],"central":[48],"pattern":[49],"generator":[50],"for":[52],"biped":[54],"locomotion.":[55],"A":[56],"parameter":[58],"constant":[61],"input":[62],"from":[63],"higher":[64],"motor":[65],"centers.":[66],"Numerical":[67],"calculations":[68],"show":[69],"system":[71,140],"successfully":[72],"expresses":[73],"some":[74],"characteristic":[75],"behaviors,":[76],"were":[78,88],"obtained":[79],"by":[80,98,119,133],"more":[81],"complicated":[82],"Fitzhugh-Nagumo":[83],"oscillator":[84],"model,":[85],"and":[86,111,132],"found":[89],"in":[90],"clinical":[91],"data":[92],"disordered":[94],"interlimb":[95],"coordination":[96],"caused":[97],"Parkinson's":[99],"disease.":[100],"The":[101],"observed":[102],"results":[103],"symmetric":[105],"anti":[106],"-phase":[107],"synchronization,":[108,110],"asymmetric":[109],"breakdown":[112],"synchronization":[115,135],"can":[116],"be":[117],"explained":[118],"existence":[121],"condition":[122,136],"energy":[125],"function":[126],"neural":[130],"network,":[131],"coupled":[139],"phase":[142],"oscillators.":[143]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
