{"id":"https://openalex.org/W4386411170","doi":"https://doi.org/10.1142/s0218127423300252","title":"Bifurcations of Mode-Locked Periodic Orbits in Three-Dimensional Maps","display_name":"Bifurcations of Mode-Locked Periodic Orbits in Three-Dimensional Maps","publication_year":2023,"publication_date":"2023-08-01","ids":{"openalex":"https://openalex.org/W4386411170","doi":"https://doi.org/10.1142/s0218127423300252"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127423300252","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127423300252","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/A5050957618","display_name":"Sishu Shankar Muni","orcid":"https://orcid.org/0000-0001-9545-8345"},"institutions":[{"id":"https://openalex.org/I127439422","display_name":"Indian Institute of Science Education and Research Kolkata","ror":"https://ror.org/00djv2c17","country_code":"IN","type":"education","lineage":["https://openalex.org/I127439422"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Sishu Shankar Muni","raw_affiliation_strings":["Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Campus Road, Mohanpur, West Bengal 741246, India"],"affiliations":[{"raw_affiliation_string":"Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Campus Road, Mohanpur, West Bengal 741246, India","institution_ids":["https://openalex.org/I127439422"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074868206","display_name":"Soumitro Banerjee","orcid":"https://orcid.org/0000-0003-3576-0846"},"institutions":[{"id":"https://openalex.org/I127439422","display_name":"Indian Institute of Science Education and Research Kolkata","ror":"https://ror.org/00djv2c17","country_code":"IN","type":"education","lineage":["https://openalex.org/I127439422"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Soumitro Banerjee","raw_affiliation_strings":["Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Campus Road, Mohanpur, West Bengal 741246, India"],"affiliations":[{"raw_affiliation_string":"Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Campus Road, Mohanpur, West Bengal 741246, India","institution_ids":["https://openalex.org/I127439422"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5050957618"],"corresponding_institution_ids":["https://openalex.org/I127439422"],"apc_list":null,"apc_paid":null,"fwci":6.1564,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.97617269,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"33","issue":"10","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9987999796867371,"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"}},"topics":[{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9987999796867371,"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"}},{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9923999905586243,"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":0.9869999885559082,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.707627534866333},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.706276535987854},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.6784451603889465},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.6397362947463989},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.6311557292938232},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6044704914093018},{"id":"https://openalex.org/keywords/periodic-orbits","display_name":"Periodic orbits","score":0.5988997220993042},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5654487013816833},{"id":"https://openalex.org/keywords/torus","display_name":"Torus","score":0.5275371074676514},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5182442665100098},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4719088673591614},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.47129952907562256},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.4633975327014923},{"id":"https://openalex.org/keywords/sign","display_name":"Sign (mathematics)","score":0.4357500374317169},{"id":"https://openalex.org/keywords/period-doubling-bifurcation","display_name":"Period-doubling bifurcation","score":0.43126627802848816},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.43061378598213196},{"id":"https://openalex.org/keywords/floquet-theory","display_name":"Floquet theory","score":0.41980475187301636},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3361471891403198},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.30791887640953064},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1731891632080078},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.09793636202812195}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.707627534866333},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.706276535987854},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.6784451603889465},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.6397362947463989},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.6311557292938232},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6044704914093018},{"id":"https://openalex.org/C2984157986","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Periodic orbits","level":2,"score":0.5988997220993042},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5654487013816833},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.5275371074676514},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5182442665100098},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4719088673591614},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.47129952907562256},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.4633975327014923},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.4357500374317169},{"id":"https://openalex.org/C194271172","wikidata":"https://www.wikidata.org/wiki/Q2181373","display_name":"Period-doubling bifurcation","level":4,"score":0.43126627802848816},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.43061378598213196},{"id":"https://openalex.org/C55649039","wikidata":"https://www.wikidata.org/wiki/Q902618","display_name":"Floquet theory","level":3,"score":0.41980475187301636},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3361471891403198},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.30791887640953064},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1731891632080078},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.09793636202812195},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","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:10.1142/s0218127423300252","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127423300252","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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1965175174","https://openalex.org/W1973071104","https://openalex.org/W1976052480","https://openalex.org/W1983191768","https://openalex.org/W1989438722","https://openalex.org/W1999587814","https://openalex.org/W2007257097","https://openalex.org/W2014914021","https://openalex.org/W2015609215","https://openalex.org/W2024100940","https://openalex.org/W2026401874","https://openalex.org/W2031035886","https://openalex.org/W2031812691","https://openalex.org/W2051651497","https://openalex.org/W2056964900","https://openalex.org/W2058561817","https://openalex.org/W2060651243","https://openalex.org/W2063137023","https://openalex.org/W2064398406","https://openalex.org/W2067607110","https://openalex.org/W2071945827","https://openalex.org/W2094656677","https://openalex.org/W2099993067","https://openalex.org/W2113996820","https://openalex.org/W2120417009","https://openalex.org/W2130159712","https://openalex.org/W2285692442","https://openalex.org/W2469363212","https://openalex.org/W3102882131","https://openalex.org/W3119170784","https://openalex.org/W3120415512","https://openalex.org/W3211522089","https://openalex.org/W3213211982","https://openalex.org/W4293873725"],"related_works":["https://openalex.org/W2950189493","https://openalex.org/W2352382011","https://openalex.org/W4256126201","https://openalex.org/W2359237009","https://openalex.org/W2066781911","https://openalex.org/W2166919819","https://openalex.org/W3119049163","https://openalex.org/W4366734142","https://openalex.org/W3187012233","https://openalex.org/W4287071020"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"report":[4,105],"the":[5,37,41,45,63,70,73,82,91,97,100,106,114,139,146],"bifurcations":[6],"of":[7,14,36,44,51,53,72,84,93,99,110,113,129],"mode-locked":[8],"periodic":[9],"orbits":[10],"occurring":[11],"in":[12,27],"maps":[13],"three":[15],"or":[16],"higher":[17],"dimensions.":[18],"The":[19],"\u201ctorus\u201d":[20],"is":[21,77],"represented":[22],"by":[23],"a":[24],"closed":[25,74,122],"loop":[26],"discrete":[28],"time,":[29],"which":[30,88,119,133],"contains":[31],"stable":[32,115,140],"and":[33,40,62,68,86,116,150],"unstable":[34,42],"cycles":[35],"same":[38],"periodicity,":[39],"manifolds":[43],"saddle.":[46],"We":[47,103,125],"investigate":[48],"two":[49,57],"types":[50,128],"\u201cdoubling\u201d":[52],"such":[54],"loops:":[55],"(a)":[56],"disjoint":[58],"loops":[59],"are":[60],"created":[61],"iterates":[64],"toggle":[65],"between":[66],"them,":[67],"(b)":[69],"length":[71],"invariant":[75,123],"curve":[76],"doubled.":[78],"Our":[79],"work":[80],"supports":[81],"conjecture":[83],"Gardini":[85],"Sushko,":[87],"says":[89],"that":[90],"type":[92],"bifurcation":[94,112],"depends":[95],"on":[96],"sign":[98],"third":[101],"eigenvalue.":[102],"also":[104],"situation":[107],"arising":[108],"out":[109],"Neimark\u2013Sacker":[111],"saddle":[117,147],"cycles,":[118],"creates":[120],"cyclic":[121],"curves.":[124],"show":[126],"interesting":[127],"saddle-node":[130],"connection":[131],"structures,":[132],"emerge":[134],"for":[135],"parameter":[136],"values":[137],"where":[138],"fixed":[141],"point":[142],"has":[143,148],"bifurcated":[144],"but":[145],"not,":[149],"vice":[151],"versa.":[152]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":9}],"updated_date":"2025-12-19T19:40:27.379048","created_date":"2025-10-10T00:00:00"}