{"id":"https://openalex.org/W2028772246","doi":"https://doi.org/10.1142/s0218127408021580","title":"GENERATION OF A FOUR-WING CHAOTIC ATTRACTOR BY TWO WEAKLY-COUPLED LORENZ SYSTEMS","display_name":"GENERATION OF A FOUR-WING CHAOTIC ATTRACTOR BY TWO WEAKLY-COUPLED LORENZ SYSTEMS","publication_year":2008,"publication_date":"2008-07-01","ids":{"openalex":"https://openalex.org/W2028772246","doi":"https://doi.org/10.1142/s0218127408021580","mag":"2028772246"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127408021580","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127408021580","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/A5055199720","display_name":"Giuseppe Grassi","orcid":"https://orcid.org/0000-0002-8876-3760"},"institutions":[{"id":"https://openalex.org/I141649380","display_name":"Western Michigan University","ror":"https://ror.org/04j198w64","country_code":"US","type":"education","lineage":["https://openalex.org/I141649380"]},{"id":"https://openalex.org/I142910587","display_name":"University of Salento","ror":"https://ror.org/03fc1k060","country_code":"IT","type":"education","lineage":["https://openalex.org/I142910587"]}],"countries":["IT","US"],"is_corresponding":false,"raw_author_name":"GIUSEPPE GRASSI","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Western Michigan University, Kalamazoo, MI 49008, USA","Dipartimento di Ingegneria dell'Innovazione, Universit\u00e0 del Salento, 73100 Lecce, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Western Michigan University, Kalamazoo, MI 49008, USA","institution_ids":["https://openalex.org/I141649380"]},{"raw_affiliation_string":"Dipartimento di Ingegneria dell'Innovazione, Universit\u00e0 del Salento, 73100 Lecce, Italy","institution_ids":["https://openalex.org/I142910587"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032858247","display_name":"Frank L. Severance","orcid":null},"institutions":[{"id":"https://openalex.org/I141649380","display_name":"Western Michigan University","ror":"https://ror.org/04j198w64","country_code":"US","type":"education","lineage":["https://openalex.org/I141649380"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"FRANK L. SEVERANCE","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Western Michigan University, Kalamazoo, MI 49008, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Western Michigan University, Kalamazoo, MI 49008, USA","institution_ids":["https://openalex.org/I141649380"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039790779","display_name":"EMIL D. MASHEV","orcid":null},"institutions":[{"id":"https://openalex.org/I141649380","display_name":"Western Michigan University","ror":"https://ror.org/04j198w64","country_code":"US","type":"education","lineage":["https://openalex.org/I141649380"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"EMIL D. MASHEV","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Western Michigan University, Kalamazoo, MI 49008, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Western Michigan University, Kalamazoo, MI 49008, USA","institution_ids":["https://openalex.org/I141649380"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028074094","display_name":"Bradley J. Bazuin","orcid":"https://orcid.org/0000-0002-3638-3176"},"institutions":[{"id":"https://openalex.org/I141649380","display_name":"Western Michigan University","ror":"https://ror.org/04j198w64","country_code":"US","type":"education","lineage":["https://openalex.org/I141649380"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"BRADLEY J. BAZUIN","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Western Michigan University, Kalamazoo, MI 49008, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Western Michigan University, Kalamazoo, MI 49008, USA","institution_ids":["https://openalex.org/I141649380"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069957952","display_name":"D.A. Miller","orcid":null},"institutions":[{"id":"https://openalex.org/I141649380","display_name":"Western Michigan University","ror":"https://ror.org/04j198w64","country_code":"US","type":"education","lineage":["https://openalex.org/I141649380"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"DAMON A. MILLER","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Western Michigan University, Kalamazoo, MI 49008, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Western Michigan University, Kalamazoo, MI 49008, USA","institution_ids":["https://openalex.org/I141649380"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.2104,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.87398971,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"18","issue":"07","first_page":"2089","last_page":"2094"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9902999997138977,"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":0.9897000193595886,"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/attractor","display_name":"Attractor","score":0.906919002532959},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.6776196360588074},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6760927438735962},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6555171012878418},{"id":"https://openalex.org/keywords/complex-conjugate","display_name":"Complex conjugate","score":0.6028867959976196},{"id":"https://openalex.org/keywords/lorenz-system","display_name":"Lorenz system","score":0.5422689318656921},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.5043257474899292},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5007152557373047},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4895089864730835},{"id":"https://openalex.org/keywords/topological-conjugacy","display_name":"Topological conjugacy","score":0.4170284867286682},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3517804741859436},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.24752551317214966},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.22107109427452087},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13072574138641357}],"concepts":[{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.906919002532959},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.6776196360588074},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6760927438735962},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6555171012878418},{"id":"https://openalex.org/C45542137","wikidata":"https://www.wikidata.org/wiki/Q381040","display_name":"Complex conjugate","level":2,"score":0.6028867959976196},{"id":"https://openalex.org/C151510863","wikidata":"https://www.wikidata.org/wiki/Q899844","display_name":"Lorenz system","level":3,"score":0.5422689318656921},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.5043257474899292},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5007152557373047},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4895089864730835},{"id":"https://openalex.org/C165263651","wikidata":"https://www.wikidata.org/wiki/Q2443460","display_name":"Topological conjugacy","level":2,"score":0.4170284867286682},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3517804741859436},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.24752551317214966},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.22107109427452087},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13072574138641357},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"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/s0218127408021580","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127408021580","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":19,"referenced_works":["https://openalex.org/W1572030142","https://openalex.org/W1974095580","https://openalex.org/W1976519394","https://openalex.org/W1976791164","https://openalex.org/W1988843508","https://openalex.org/W1996069912","https://openalex.org/W1999534682","https://openalex.org/W2034421105","https://openalex.org/W2047077576","https://openalex.org/W2066910975","https://openalex.org/W2107883576","https://openalex.org/W2122076389","https://openalex.org/W2127160608","https://openalex.org/W2141394518","https://openalex.org/W2152532612","https://openalex.org/W2162022992","https://openalex.org/W2165801592","https://openalex.org/W4206744643","https://openalex.org/W4253211883"],"related_works":["https://openalex.org/W4289542543","https://openalex.org/W2891065597","https://openalex.org/W3158046166","https://openalex.org/W1509796342","https://openalex.org/W1742246664","https://openalex.org/W2033042940","https://openalex.org/W2089902280","https://openalex.org/W2145782975","https://openalex.org/W2810701175","https://openalex.org/W242476103"],"abstract_inverted_index":{"This":[0],"paper":[1,76],"presents":[2],"a":[3],"novel":[4],"chaotic":[5],"four-wing":[6],"attractor":[7,61,85,106],"generated":[8],"by":[9],"coupling":[10],"two":[11,56,66],"identical":[12],"Lorenz":[13,52],"systems.":[14],"An":[15],"analysis":[16],"of":[17,37,45,58,72,82,98],"the":[18,35,38,43,50,55,59,65,69,79,99],"proposed":[19,100],"system":[20,101],"shows":[21,77],"that":[22,78],"its":[23],"equilibria":[24,67,90],"have":[25],"certain":[26],"symmetries":[27],"with":[28,49,68,91],"respect":[29],"to":[30,102],"specific":[31],"coordinate":[32],"planes":[33],"and":[34],"eigenvalues":[36],"associated":[39],"Jacobian":[40],"matrices":[41],"exhibit":[42],"property":[44],"similarity.":[46],"In":[47],"analogy":[48],"original":[51],"system,":[53],"where":[54],"wings":[57,81],"butterfly":[60],"are":[62,86],"located":[63,87],"around":[64,88],"unstable":[70,93],"pair":[71],"complex-conjugate":[73,94],"eigenvalues,":[74],"this":[75,83],"four":[80,89,92],"new":[84],"eigenvalues.":[95],"A":[96],"generalization":[97],"realize":[103],"an":[104],"eight-wing":[105],"is":[107],"also":[108],"described.":[109]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
