{"id":"https://openalex.org/W2033373083","doi":"https://doi.org/10.1109/tcsi.2012.2188947","title":"Rigorous Study of the Chua's Circuit Spiral Attractor","display_name":"Rigorous Study of the Chua's Circuit Spiral Attractor","publication_year":2012,"publication_date":"2012-04-11","ids":{"openalex":"https://openalex.org/W2033373083","doi":"https://doi.org/10.1109/tcsi.2012.2188947","mag":"2033373083"},"language":"en","primary_location":{"id":"doi:10.1109/tcsi.2012.2188947","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2012.2188947","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Circuits and Systems I: Regular Papers","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/A5037161015","display_name":"Zbigniew Galias","orcid":"https://orcid.org/0000-0001-7253-7075"},"institutions":[{"id":"https://openalex.org/I686019","display_name":"AGH University of Krakow","ror":"https://ror.org/00bas1c41","country_code":"PL","type":"education","lineage":["https://openalex.org/I686019"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Zbigniew Galias","raw_affiliation_strings":["Department of Electrical Engineering, AGH University of Science and Technology, Krakow, Poland","[Department of Electrical Engineering, AGH University of Science and Technology, Krak\u00f3w, Poland]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, AGH University of Science and Technology, Krakow, Poland","institution_ids":["https://openalex.org/I686019"]},{"raw_affiliation_string":"[Department of Electrical Engineering, AGH University of Science and Technology, Krak\u00f3w, Poland]","institution_ids":["https://openalex.org/I686019"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5037161015"],"corresponding_institution_ids":["https://openalex.org/I686019"],"apc_list":null,"apc_paid":null,"fwci":0.7113,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.6967354,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"59","issue":"10","first_page":"2374","last_page":"2382"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9994999766349792,"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":0.9994999766349792,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9994999766349792,"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":0.9980999827384949,"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/attractor","display_name":"Attractor","score":0.8448129296302795},{"id":"https://openalex.org/keywords/hyperplane","display_name":"Hyperplane","score":0.6888626217842102},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.6341000199317932},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.5876355171203613},{"id":"https://openalex.org/keywords/chuas-circuit","display_name":"Chua's circuit","score":0.5303201079368591},{"id":"https://openalex.org/keywords/spiral","display_name":"Spiral (railway)","score":0.5114147067070007},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5041021108627319},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4916735291481018},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46374401450157166},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.42049503326416016},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3570480942726135},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3543691635131836},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34904050827026367},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33024168014526367},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.26888948678970337},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.15957993268966675},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.11678236722946167},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10514417290687561}],"concepts":[{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.8448129296302795},{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.6888626217842102},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.6341000199317932},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.5876355171203613},{"id":"https://openalex.org/C2781300247","wikidata":"https://www.wikidata.org/wiki/Q258022","display_name":"Chua's circuit","level":3,"score":0.5303201079368591},{"id":"https://openalex.org/C174128100","wikidata":"https://www.wikidata.org/wiki/Q846907","display_name":"Spiral (railway)","level":2,"score":0.5114147067070007},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5041021108627319},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4916735291481018},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46374401450157166},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.42049503326416016},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3570480942726135},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3543691635131836},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34904050827026367},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33024168014526367},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.26888948678970337},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.15957993268966675},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.11678236722946167},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10514417290687561},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","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},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcsi.2012.2188947","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2012.2188947","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Circuits and Systems I: Regular Papers","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":13,"referenced_works":["https://openalex.org/W401634476","https://openalex.org/W1523589238","https://openalex.org/W1964154886","https://openalex.org/W1966278929","https://openalex.org/W2011687450","https://openalex.org/W2036805518","https://openalex.org/W2042388195","https://openalex.org/W2077157707","https://openalex.org/W2112799776","https://openalex.org/W2116658875","https://openalex.org/W2171987742","https://openalex.org/W2963701132","https://openalex.org/W3209416867"],"related_works":["https://openalex.org/W1995550449","https://openalex.org/W2801748458","https://openalex.org/W2765787715","https://openalex.org/W327886041","https://openalex.org/W2612801513","https://openalex.org/W2065885758","https://openalex.org/W2063319139","https://openalex.org/W879289140","https://openalex.org/W4312668142","https://openalex.org/W3210265797"],"abstract_inverted_index":{"It":[0],"is":[1,7,63],"shown":[2],"that":[3],"a":[4],"certain":[5],"set":[6,20],"positively":[8],"invariant":[9],"for":[10,39],"the":[11,16,22,25,31,34,54,61],"return":[12,35],"map":[13],"associated":[14],"with":[15],"Chua's":[17],"circuit.":[18],"The":[19],"contains":[21],"intersection":[23],"of":[24,42],"numerically":[26],"observed":[27],"spiral":[28],"attractor":[29],"and":[30],"planes":[32],"defining":[33],"map.":[36],"A":[37],"method":[38],"rigorous":[40],"integration":[41],"piece-wise":[43],"linear":[44,55],"systems":[45],"in":[46],"regions":[47,56],"containing":[48],"trajectories":[49],"tangent":[50],"to":[51,58],"hyperplanes":[52],"separating":[53],"necessary":[57],"carry":[59],"out":[60],"proof":[62],"developed.":[64]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}