{"id":"https://openalex.org/W1982210304","doi":"https://doi.org/10.1142/s0218127413300322","title":"ALGORITHMS FOR OBTAINING A SADDLE TORUS BETWEEN TWO ATTRACTORS","display_name":"ALGORITHMS FOR OBTAINING A SADDLE TORUS BETWEEN TWO ATTRACTORS","publication_year":2013,"publication_date":"2013-09-01","ids":{"openalex":"https://openalex.org/W1982210304","doi":"https://doi.org/10.1142/s0218127413300322","mag":"1982210304"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127413300322","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127413300322","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077189330","display_name":"Kyohei Kamiyama","orcid":null},"institutions":[{"id":"https://openalex.org/I16656306","display_name":"Meiji University","ror":"https://ror.org/02rqvrp93","country_code":"JP","type":"education","lineage":["https://openalex.org/I16656306"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"KYOHEI KAMIYAMA","raw_affiliation_strings":["Department of Electronics and Bioinformatics, Meiji University, 1-1-1 Higashi-Mita, Tama-ku, Kawasaki-shi, Kanagawa 214-8571, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronics and Bioinformatics, Meiji University, 1-1-1 Higashi-Mita, Tama-ku, Kawasaki-shi, Kanagawa 214-8571, Japan","institution_ids":["https://openalex.org/I16656306"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103708667","display_name":"Motomasa Komuro","orcid":"https://orcid.org/0009-0009-2304-590X"},"institutions":[{"id":"https://openalex.org/I144705627","display_name":"Teikyo University of Science","ror":"https://ror.org/025vmw012","country_code":"JP","type":"education","lineage":["https://openalex.org/I144705627"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"MOTOMASA KOMURO","raw_affiliation_strings":["Center for Fundamental Education, Teikyo University of Science, 2525 Yatsusawa, Uenohara-shi, Yamanashi 409-0193, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Fundamental Education, Teikyo University of Science, 2525 Yatsusawa, Uenohara-shi, Yamanashi 409-0193, Japan","institution_ids":["https://openalex.org/I144705627"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111950350","display_name":"Tetsuro Endo","orcid":null},"institutions":[{"id":"https://openalex.org/I16656306","display_name":"Meiji University","ror":"https://ror.org/02rqvrp93","country_code":"JP","type":"education","lineage":["https://openalex.org/I16656306"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"TETSURO ENDO","raw_affiliation_strings":["Department of Electronics and Bioinformatics, Meiji University, 1-1-1 Higashi-Mita, Tama-ku, Kawasaki-shi, Kanagawa 214-8571, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronics and Bioinformatics, Meiji University, 1-1-1 Higashi-Mita, Tama-ku, Kawasaki-shi, Kanagawa 214-8571, Japan","institution_ids":["https://openalex.org/I16656306"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.0261,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.94045082,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"23","issue":"09","first_page":"1330032","last_page":"1330032"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9994999766349792,"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":0.9994999766349792,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9975000023841858,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9876000285148621,"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/torus","display_name":"Torus","score":0.8610731363296509},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.8318126201629639},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.6662472486495972},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.62093186378479},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.6043681502342224},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.5814425945281982},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43163472414016724},{"id":"https://openalex.org/keywords/lorenz-system","display_name":"Lorenz system","score":0.42922282218933105},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.41953718662261963},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3666178584098816},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35721009969711304},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.27516472339630127},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20290878415107727},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.12951752543449402},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.10886281728744507}],"concepts":[{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.8610731363296509},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.8318126201629639},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.6662472486495972},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.62093186378479},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.6043681502342224},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.5814425945281982},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43163472414016724},{"id":"https://openalex.org/C151510863","wikidata":"https://www.wikidata.org/wiki/Q899844","display_name":"Lorenz system","level":3,"score":0.42922282218933105},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.41953718662261963},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3666178584098816},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35721009969711304},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.27516472339630127},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20290878415107727},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.12951752543449402},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.10886281728744507},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127413300322","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127413300322","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1802803383","display_name":"Analysis of the behavior of MMOs under weak noise","funder_award_id":"24560556","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320325855","display_name":"Council for Science and Technology Policy","ror":null},{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1970650503","https://openalex.org/W1998630995","https://openalex.org/W2064148786","https://openalex.org/W2066959861","https://openalex.org/W2071333933","https://openalex.org/W2096899223","https://openalex.org/W2121065739","https://openalex.org/W2152958597"],"related_works":["https://openalex.org/W4289542543","https://openalex.org/W2538665745","https://openalex.org/W2891065597","https://openalex.org/W1509796342","https://openalex.org/W1742246664","https://openalex.org/W3158046166","https://openalex.org/W2033042940","https://openalex.org/W2089902280","https://openalex.org/W2145782975","https://openalex.org/W2810701175"],"abstract_inverted_index":{"We":[0,110,151],"develop":[1],"two":[2,12,113,116,137,146],"algorithms":[3,114],"for":[4,46,115],"obtaining":[5],"an":[6,81],"index":[7],"1":[8],"saddle":[9,129,159],"torus":[10,57,130],"between":[11],"attractors":[13],"of":[14,80,105,122,135,144,156],"which":[15,29,66],"basin":[16,133],"boundary":[17,134],"is":[18,88,100,127,143],"smooth":[19],"by":[20],"using":[21],"the":[22,26,63,86,106,132,136,141,145,153,157],"bisection":[23],"method.":[24,109],"In":[25,62,83],"first":[27],"algorithm,":[28,65,85],"we":[30,35,67,72],"name":[31,68],"\"overall":[32],"template":[33,38,70,75,108],"method\",":[34,71],"make":[36,73],"a":[37,40,53,56,60,74,78,91,95,120,128],"approximating":[39,76],"whole":[41],"attractor":[42,50,87],"and":[43,58,94,140,161],"use":[44],"it":[45],"pattern":[47],"matching.":[48],"The":[49],"can":[51],"be":[52],"periodic":[54,92],"orbit,":[55],"even":[59],"chaos.":[61],"second":[64],"\"partial":[69],"only":[77],"part":[79],"attractor.":[82],"this":[84],"restricted":[89],"to":[90],"orbit":[93],"two-torus,":[96],"but":[97],"calculation":[98],"time":[99],"much":[101],"smaller":[102],"than":[103],"that":[104],"overall":[107],"demonstrate":[111],"these":[112],"solutions,":[117,139],"observed":[118],"in":[119,131],"ring":[121],"six-coupled":[123],"bistable":[124],"oscillators.":[125],"One":[126],"switching":[138],"other":[142],"quasi-periodic":[147],"propagating":[148],"wave":[149],"solutions.":[150],"calculate":[152],"Lyapunov":[154,165],"spectrum":[155],"obtained":[158],"torus,":[160],"confirm":[162],"one":[163],"positive":[164],"exponent.":[166]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":5}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}