{"id":"https://openalex.org/W1982703848","doi":"https://doi.org/10.1142/s0218127413501368","title":"DYNAMICS OF THE MUTHUSWAMY\u2013CHUA SYSTEM","display_name":"DYNAMICS OF THE MUTHUSWAMY\u2013CHUA SYSTEM","publication_year":2013,"publication_date":"2013-08-01","ids":{"openalex":"https://openalex.org/W1982703848","doi":"https://doi.org/10.1142/s0218127413501368","mag":"1982703848"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127413501368","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127413501368","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/A5101759180","display_name":"Yuanfan Zhang","orcid":"https://orcid.org/0009-0008-5866-4906"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"YUANFAN ZHANG","raw_affiliation_strings":["UM-SJTU Joint Institute, Shanghai Jiao Tong University, Shanghai 200240, P. R. China","UM-SJTU Joint Institute, Shanghai Jiao Tong University, Shanghai, 200240, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UM-SJTU Joint Institute, Shanghai Jiao Tong University, Shanghai 200240, P. R. China","institution_ids":["https://openalex.org/I183067930"]},{"raw_affiliation_string":"UM-SJTU Joint Institute, Shanghai Jiao Tong University, Shanghai, 200240, P. R. China","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100368854","display_name":"Xiang Zhang","orcid":"https://orcid.org/0000-0002-3272-894X"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"XIANG ZHANG","raw_affiliation_strings":["Department of Mathematics, and MOE-LSC, Shanghai Jiao Tong University, Shanghai 200240, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, and MOE-LSC, Shanghai Jiao Tong University, Shanghai 200240, P. R. China","institution_ids":["https://openalex.org/I183067930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I183067930"],"apc_list":null,"apc_paid":null,"fwci":1.2223,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.78587144,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"23","issue":"08","first_page":"1350136","last_page":"1350136"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9988999962806702,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9988999962806702,"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/T10244","display_name":"Chaos control and synchronization","score":0.9983999729156494,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9977999925613403,"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/attractor","display_name":"Attractor","score":0.795479416847229},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.7285454273223877},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5985283255577087},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.5769139528274536},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.5487079620361328},{"id":"https://openalex.org/keywords/periodic-orbits","display_name":"Periodic orbits","score":0.5454086661338806},{"id":"https://openalex.org/keywords/orbit","display_name":"Orbit (dynamics)","score":0.44692063331604004},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4319482743740082},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4245983958244324},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.40313559770584106},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3643043637275696},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.2778128683567047},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.14861345291137695},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1428857445716858}],"concepts":[{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.795479416847229},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.7285454273223877},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5985283255577087},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.5769139528274536},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.5487079620361328},{"id":"https://openalex.org/C2984157986","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Periodic orbits","level":2,"score":0.5454086661338806},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.44692063331604004},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4319482743740082},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4245983958244324},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40313559770584106},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3643043637275696},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.2778128683567047},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.14861345291137695},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1428857445716858},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127413501368","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127413501368","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":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320338368","display_name":"FP7 People: Marie-Curie Actions","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1997394516","https://openalex.org/W2005315940","https://openalex.org/W2041627097","https://openalex.org/W2052746052","https://openalex.org/W2054967352","https://openalex.org/W2104604364","https://openalex.org/W2171161332"],"related_works":["https://openalex.org/W2379488025","https://openalex.org/W2318462079","https://openalex.org/W2585728124","https://openalex.org/W2169362996","https://openalex.org/W2340294931","https://openalex.org/W2565482338","https://openalex.org/W2001163940","https://openalex.org/W2121212734","https://openalex.org/W2082884906","https://openalex.org/W3014531371"],"abstract_inverted_index":{"The":[0],"Muthuswamy\u2013Chua":[1],"system":[2,33,63],"[Formula:":[3],"see":[4],"text]":[5],"describes":[6],"the":[7,22,32,62,77],"simplest":[8],"electronic":[9],"circuit":[10],"which":[11,40,106,112],"can":[12],"have":[13],"chaotic":[14,70],"phenomena.":[15],"In":[16],"this":[17],"paper,":[18],"we":[19,54,97],"first":[20],"prove":[21,55],"existence":[23],"of":[24,27,31,39,76,101],"three":[25],"families":[26],"consecutive":[28,44],"periodic":[29,66],"orbits":[30],"when":[34],"\u03b1":[35,58],"=":[36,80,84],"0,":[37],"two":[38,49],"are":[41,107,113],"located":[42],"on":[43],"invariant":[45,50,103],"surfaces":[46],"and":[47,82,111],"form":[48],"topological":[51,104],"cylinders.":[52],"Then":[53],"that":[56],"for":[57],">":[59],"0":[60,81],"if":[61],"has":[64],"a":[65,69,95],"orbit":[67],"or":[68],"attractor,":[71],"it":[72],"must":[73],"intersect":[74],"both":[75],"planes":[78],"z":[79,83],"-1":[85],"infinitely":[86],"many":[87],"times":[88],"as":[89],"t":[90],"tends":[91],"to":[92],"infinity.":[93],"As":[94],"byproduct,":[96],"get":[98],"an":[99],"example":[100],"unstable":[102],"cylinders":[105],"not":[108],"normally":[109],"hyperbolic":[110],"also":[114],"destroyed":[115],"under":[116],"small":[117],"perturbations.":[118]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}