{"id":"https://openalex.org/W2103748903","doi":"https://doi.org/10.1142/s0218127414500345","title":"Coexisting Hidden Attractors in a 4-D Simplified Lorenz System","display_name":"Coexisting Hidden Attractors in a 4-D Simplified Lorenz System","publication_year":2014,"publication_date":"2014-03-01","ids":{"openalex":"https://openalex.org/W2103748903","doi":"https://doi.org/10.1142/s0218127414500345","mag":"2103748903"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127414500345","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127414500345","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/A5031215480","display_name":"Chunbiao Li","orcid":"https://orcid.org/0000-0002-9932-0914"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]},{"id":"https://openalex.org/I4210104733","display_name":"Jiangsu Vocational Institute of Commerce","ror":"https://ror.org/01aew1m62","country_code":"CN","type":"other","lineage":["https://openalex.org/I4210104733"]},{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN","US"],"is_corresponding":false,"raw_author_name":"Chunbiao Li","raw_affiliation_strings":["Department of Physics, University of Wisconsin\u2013Madison, Madison, WI 53706, USA","Engineering Technology Research and Development Center of Jiangsu Circulation Modernization Sensor Network, Jiangsu Institute of Commerce, Nanjing 210007, P. R. China","School of Information Science and Engineering, Southeast University, Nanjing 210096, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, University of Wisconsin\u2013Madison, Madison, WI 53706, USA","institution_ids":["https://openalex.org/I135310074"]},{"raw_affiliation_string":"Engineering Technology Research and Development Center of Jiangsu Circulation Modernization Sensor Network, Jiangsu Institute of Commerce, Nanjing 210007, P. R. China","institution_ids":["https://openalex.org/I4210104733"]},{"raw_affiliation_string":"School of Information Science and Engineering, Southeast University, Nanjing 210096, P. R. China","institution_ids":["https://openalex.org/I76569877"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081308615","display_name":"J. C. Sprott","orcid":"https://orcid.org/0000-0001-7014-3283"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. C. Sprott","raw_affiliation_strings":["Department of Physics, University of Wisconsin\u2013Madison, Madison, WI 53706, USA","Department of Physics, University of Wisconsin, Madison, Madison, WI 53706, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, University of Wisconsin\u2013Madison, Madison, WI 53706, USA","institution_ids":["https://openalex.org/I135310074"]},{"raw_affiliation_string":"Department of Physics, University of Wisconsin, Madison, Madison, WI 53706, USA","institution_ids":["https://openalex.org/I135310074"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":19.5439,"has_fulltext":false,"cited_by_count":282,"citation_normalized_percentile":{"value":0.99666746,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"24","issue":"03","first_page":"1450034","last_page":"1450034"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9983000159263611,"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":0.9961000084877014,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.8377128839492798},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.6764443516731262},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.6700196266174316},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.656924843788147},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.6168774366378784},{"id":"https://openalex.org/keywords/parameter-space","display_name":"Parameter space","score":0.5876027345657349},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5737156867980957},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5223796963691711},{"id":"https://openalex.org/keywords/torus","display_name":"Torus","score":0.48790618777275085},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.47685205936431885},{"id":"https://openalex.org/keywords/fractal","display_name":"Fractal","score":0.4720388650894165},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.45384424924850464},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.44042155146598816},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4250306487083435},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.41582125425338745},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.36128202080726624},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3133143186569214},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2382248342037201},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14121872186660767},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.11818060278892517},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1044272780418396}],"concepts":[{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.8377128839492798},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.6764443516731262},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.6700196266174316},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.656924843788147},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.6168774366378784},{"id":"https://openalex.org/C73586568","wikidata":"https://www.wikidata.org/wiki/Q2600211","display_name":"Parameter space","level":2,"score":0.5876027345657349},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5737156867980957},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5223796963691711},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.48790618777275085},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.47685205936431885},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.4720388650894165},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.45384424924850464},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.44042155146598816},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4250306487083435},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41582125425338745},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.36128202080726624},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3133143186569214},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2382248342037201},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14121872186660767},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.11818060278892517},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1044272780418396},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127414500345","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127414500345","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":22,"referenced_works":["https://openalex.org/W1542193783","https://openalex.org/W1964044133","https://openalex.org/W1975085179","https://openalex.org/W1990027217","https://openalex.org/W1998630995","https://openalex.org/W2009483907","https://openalex.org/W2031668778","https://openalex.org/W2055644003","https://openalex.org/W2065644906","https://openalex.org/W2074884842","https://openalex.org/W2107523717","https://openalex.org/W2123893676","https://openalex.org/W2135413047","https://openalex.org/W2136221998","https://openalex.org/W2141394518","https://openalex.org/W2152254020","https://openalex.org/W2167380735","https://openalex.org/W2171018278","https://openalex.org/W2279520815","https://openalex.org/W2352900015","https://openalex.org/W3025560754","https://openalex.org/W4234284487"],"related_works":["https://openalex.org/W2371448224","https://openalex.org/W3134495997","https://openalex.org/W2363680170","https://openalex.org/W2376428685","https://openalex.org/W4256082577","https://openalex.org/W625783435","https://openalex.org/W2048742619","https://openalex.org/W2384641672","https://openalex.org/W2742179975","https://openalex.org/W2043619729"],"abstract_inverted_index":{"A":[0],"new":[1],"simple":[2,116],"four-dimensional":[3],"equilibrium-free":[4],"autonomous":[5],"ODE":[6],"system":[7,11],"is":[8,32],"described.":[9],"The":[10],"has":[12,26,45,82,104],"seven":[13],"terms,":[14],"two":[15,20],"quadratic":[16],"nonlinearities,":[17],"and":[18,87],"only":[19],"parameters.":[21],"Its":[22],"Jacobian":[23],"matrix":[24],"everywhere":[25],"rank":[27],"less":[28],"than":[29],"4.":[30],"It":[31],"hyperchaotic":[33],"in":[34,41,109],"some":[35],"regions":[36,43,77],"of":[37,56,64,78,102],"parameter":[38,79],"space,":[39,80],"while":[40],"other":[42,76,111],"it":[44,81],"an":[46,71],"attracting":[47],"torus":[48],"that":[49],"coexists":[50],"with":[51,60],"either":[52],"a":[53,61],"symmetric":[54,62],"pair":[55,63],"strange":[57],"attractors":[58,97],"or":[59],"limit":[65,85],"cycles":[66,86],"whose":[67],"basin":[68],"boundaries":[69],"have":[70],"intricate":[72],"fractal":[73],"structure.":[74],"In":[75],"three":[83],"coexisting":[84],"Arnold":[88],"tongues.":[89],"Since":[90],"there":[91],"are":[92,98],"no":[93],"equilibria,":[94],"all":[95],"the":[96],"hidden.":[99],"This":[100],"combination":[101],"features":[103],"not":[105],"been":[106],"previously":[107],"reported":[108],"any":[110],"system,":[112],"especially":[113],"one":[114],"as":[115,117],"this.":[118]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":14},{"year":2022,"cited_by_count":20},{"year":2021,"cited_by_count":32},{"year":2020,"cited_by_count":33},{"year":2019,"cited_by_count":30},{"year":2018,"cited_by_count":42},{"year":2017,"cited_by_count":34},{"year":2016,"cited_by_count":29},{"year":2015,"cited_by_count":22},{"year":2014,"cited_by_count":6}],"updated_date":"2026-07-31T08:31:51.225901","created_date":"2025-10-10T00:00:00"}