{"id":"https://openalex.org/W2087417978","doi":"https://doi.org/10.1142/s0218127408020835","title":"ANALYSIS OF TORUS BREAKDOWN INTO CHAOS IN A CONSTRAINT DUFFING VAN DER POL OSCILLATOR","display_name":"ANALYSIS OF TORUS BREAKDOWN INTO CHAOS IN A CONSTRAINT DUFFING VAN DER POL OSCILLATOR","publication_year":2008,"publication_date":"2008-04-01","ids":{"openalex":"https://openalex.org/W2087417978","doi":"https://doi.org/10.1142/s0218127408020835","mag":"2087417978"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127408020835","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127408020835","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://tsukuba.repo.nii.ac.jp/record/16736/files/IJBC_18-4.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084572599","display_name":"Munehisa Sekikawa","orcid":"https://orcid.org/0000-0002-5537-4734"},"institutions":[{"id":"https://openalex.org/I161296585","display_name":"Tokyo University of Science","ror":"https://ror.org/05sj3n476","country_code":"JP","type":"education","lineage":["https://openalex.org/I161296585"]},{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"MUNEHISA SEKIKAWA","raw_affiliation_strings":["Aihara Complexity Modeling Project, ERATO, JST, Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro-ku 153-8505, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Aihara Complexity Modeling Project, ERATO, JST, Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro-ku 153-8505, Japan","institution_ids":["https://openalex.org/I161296585","https://openalex.org/I74801974"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006170990","display_name":"Naohiko Inaba","orcid":"https://orcid.org/0000-0003-1153-7025"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"NAOHIKO INABA","raw_affiliation_strings":["Inaba Research Laboratory, 1-45-1 Ekihigashi-dori, Oyama-shi 323-0022, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Inaba Research Laboratory, 1-45-1 Ekihigashi-dori, Oyama-shi 323-0022, Japan","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103627370","display_name":"Takashi Tsubouchi","orcid":null},"institutions":[{"id":"https://openalex.org/I146399215","display_name":"University of Tsukuba","ror":"https://ror.org/02956yf07","country_code":"JP","type":"education","lineage":["https://openalex.org/I146399215"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"TAKASHI TSUBOUCHI","raw_affiliation_strings":["Institute of Engineering Mechanics and Systems, University of Tsukuba, 1-1-1 Ten'noudai, Tsukuba-shi 305-8573, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Engineering Mechanics and Systems, University of Tsukuba, 1-1-1 Ten'noudai, Tsukuba-shi 305-8573, Japan","institution_ids":["https://openalex.org/I146399215"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038078845","display_name":"Kazuyuki Aihara","orcid":"https://orcid.org/0000-0002-4602-9816"},"institutions":[{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"KAZUYUKI AIHARA","raw_affiliation_strings":["Institute of Industrial Science, University of Tokyo, Aihara Complexity Modeling Project, ERATO, JST, 4-6-1 Komaba, Meguro-ku 153-8505, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Industrial Science, University of Tokyo, Aihara Complexity Modeling Project, ERATO, JST, 4-6-1 Komaba, Meguro-ku 153-8505, Japan","institution_ids":["https://openalex.org/I74801974"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0179,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.75775738,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"18","issue":"04","first_page":"1051","last_page":"1068"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9962000250816345,"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"}},"topics":[{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9962000250816345,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9958999752998352,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9825999736785889,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/van-der-pol-oscillator","display_name":"Van der Pol oscillator","score":0.7493696212768555},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.6734049916267395},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.655156135559082},{"id":"https://openalex.org/keywords/intermittency","display_name":"Intermittency","score":0.6472817063331604},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6454643607139587},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.6124219298362732},{"id":"https://openalex.org/keywords/torus","display_name":"Torus","score":0.5692234635353088},{"id":"https://openalex.org/keywords/poincar\u00e9-map","display_name":"Poincar\u00e9 map","score":0.48907405138015747},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4543135166168213},{"id":"https://openalex.org/keywords/transcritical-bifurcation","display_name":"Transcritical bifurcation","score":0.42946675419807434},{"id":"https://openalex.org/keywords/homoclinic-bifurcation","display_name":"Homoclinic bifurcation","score":0.42475077509880066},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.32694557309150696},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.28199437260627747},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.22554585337638855},{"id":"https://openalex.org/keywords/turbulence","display_name":"Turbulence","score":0.10561767220497131},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.07410737872123718},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07161042094230652}],"concepts":[{"id":"https://openalex.org/C98010927","wikidata":"https://www.wikidata.org/wiki/Q2081515","display_name":"Van der Pol oscillator","level":3,"score":0.7493696212768555},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.6734049916267395},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.655156135559082},{"id":"https://openalex.org/C2780388094","wikidata":"https://www.wikidata.org/wiki/Q1666248","display_name":"Intermittency","level":3,"score":0.6472817063331604},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6454643607139587},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.6124219298362732},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.5692234635353088},{"id":"https://openalex.org/C21955772","wikidata":"https://www.wikidata.org/wiki/Q339199","display_name":"Poincar\u00e9 map","level":4,"score":0.48907405138015747},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4543135166168213},{"id":"https://openalex.org/C55610538","wikidata":"https://www.wikidata.org/wiki/Q1502581","display_name":"Transcritical bifurcation","level":5,"score":0.42946675419807434},{"id":"https://openalex.org/C155405617","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Homoclinic bifurcation","level":5,"score":0.42475077509880066},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.32694557309150696},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.28199437260627747},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.22554585337638855},{"id":"https://openalex.org/C196558001","wikidata":"https://www.wikidata.org/wiki/Q190132","display_name":"Turbulence","level":2,"score":0.10561767220497131},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.07410737872123718},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07161042094230652}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127408020835","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127408020835","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},{"id":"pmh:oai:tsukuba.repo.nii.ac.jp:00016736","is_oa":true,"landing_page_url":"http://hdl.handle.net/2241/100154","pdf_url":"https://tsukuba.repo.nii.ac.jp/record/16736/files/IJBC_18-4.pdf","source":{"id":"https://openalex.org/S4306402076","display_name":"Terrestrial Environment Research Center (University of Tsukuba)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I146399215","host_organization_name":"University of Tsukuba","host_organization_lineage":["https://openalex.org/I146399215"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:tsukuba.repo.nii.ac.jp:00016736","is_oa":true,"landing_page_url":"http://hdl.handle.net/2241/100154","pdf_url":"https://tsukuba.repo.nii.ac.jp/record/16736/files/IJBC_18-4.pdf","source":{"id":"https://openalex.org/S4306402076","display_name":"Terrestrial Environment Research Center (University of Tsukuba)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I146399215","host_organization_name":"University of Tsukuba","host_organization_lineage":["https://openalex.org/I146399215"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.46000000834465027}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2087417978.pdf"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W1553329459","https://openalex.org/W2014475702","https://openalex.org/W2020076986","https://openalex.org/W2045746056","https://openalex.org/W2050552960","https://openalex.org/W2059340344","https://openalex.org/W2069103848","https://openalex.org/W2070253541","https://openalex.org/W2073624681","https://openalex.org/W2084945542","https://openalex.org/W2094008907","https://openalex.org/W2095022822","https://openalex.org/W2095527902","https://openalex.org/W2096899223","https://openalex.org/W2107655780","https://openalex.org/W2114664913","https://openalex.org/W2143715348","https://openalex.org/W2258112886","https://openalex.org/W2333379342","https://openalex.org/W2507658679","https://openalex.org/W4239883234"],"related_works":["https://openalex.org/W2082657248","https://openalex.org/W2111166775","https://openalex.org/W2594684547","https://openalex.org/W2775656422","https://openalex.org/W2009451683","https://openalex.org/W1993086637","https://openalex.org/W2079411970","https://openalex.org/W2356715721","https://openalex.org/W2003334682","https://openalex.org/W2996450334"],"abstract_inverted_index":{"The":[0,58],"bifurcation":[1,19,97,103],"structure":[2],"of":[3],"a":[4,12,39,52,55,62,70,73,101],"constraint":[5],"Duffing":[6],"van":[7],"der":[8],"Pol":[9],"oscillator":[10],"with":[11],"diode":[13,33],"is":[14,21,34,41,49,69,82,118],"analyzed":[15],"and":[16,72,100,122],"an":[17],"objective":[18],"diagram":[20],"illustrated":[22],"in":[23,25],"detail":[24],"this":[26,44],"work.":[27],"An":[28],"idealized":[29],"case,":[30,45],"where":[31,65,76],"the":[32,46,66,77,87,96,105,109],"assumed":[35],"to":[36,108],"operate":[37],"as":[38,51],"switch,":[40],"considered.":[42],"In":[43],"Poincar\u00e9":[47],"map":[48,68,79],"constructed":[50],"one-dimensional":[53],"map:":[54],"circle":[56,67,78],"map.":[57],"parameter":[59],"boundary":[60],"between":[61],"torus-generating":[63],"region":[64,75],"diffeomorphism":[71],"chaos-generating":[74],"has":[80],"extrema":[81],"derived":[83],"explicitly,":[84],"without":[85],"solving":[86],"implicit":[88],"equations,":[89],"by":[90],"adopting":[91],"some":[92],"novel":[93],"ideas.":[94],"On":[95],"diagram,":[98],"intermittency":[99],"saddle-node":[102],"from":[104],"periodic":[106],"state":[107,111],"quasi-periodic":[110],"can":[112],"be":[113],"exactly":[114],"distinguished.":[115],"Laboratory":[116],"experiment":[117],"also":[119],"carried":[120],"out":[121],"theoretical":[123],"results":[124],"are":[125],"verified.":[126]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-08-14T07:06:38.338062","created_date":"2025-10-10T00:00:00"}