{"id":"https://openalex.org/W2026440739","doi":"https://doi.org/10.1142/s0218127413500077","title":"GLOBALLY EXPONENTIALLY ATTRACTIVE SETS AND POSITIVE INVARIANT SETS OF THREE-DIMENSIONAL AUTONOMOUS SYSTEMS WITH ONLY CROSS-PRODUCT NONLINEARITIES","display_name":"GLOBALLY EXPONENTIALLY ATTRACTIVE SETS AND POSITIVE INVARIANT SETS OF THREE-DIMENSIONAL AUTONOMOUS SYSTEMS WITH ONLY CROSS-PRODUCT NONLINEARITIES","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2026440739","doi":"https://doi.org/10.1142/s0218127413500077","mag":"2026440739"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127413500077","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127413500077","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/A5106414991","display_name":"Xinquan Zhao","orcid":null},"institutions":[{"id":"https://openalex.org/I158934434","display_name":"Zhongnan University of Economics and Law","ror":"https://ror.org/04yqxxq63","country_code":"CN","type":"education","lineage":["https://openalex.org/I158934434"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"XINQUAN ZHAO","raw_affiliation_strings":["School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, P. R. China","institution_ids":["https://openalex.org/I158934434"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100767953","display_name":"Feng Jiang","orcid":"https://orcid.org/0000-0002-4577-4646"},"institutions":[{"id":"https://openalex.org/I158934434","display_name":"Zhongnan University of Economics and Law","ror":"https://ror.org/04yqxxq63","country_code":"CN","type":"education","lineage":["https://openalex.org/I158934434"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"FENG JIANG","raw_affiliation_strings":["School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, P. R. China","institution_ids":["https://openalex.org/I158934434"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029468076","display_name":"Junhao Hu","orcid":"https://orcid.org/0000-0003-3538-2785"},"institutions":[{"id":"https://openalex.org/I174442536","display_name":"South Central University for Nationalities","ror":"https://ror.org/03d7sax13","country_code":"CN","type":"education","lineage":["https://openalex.org/I174442536"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"JUNHAO HU","raw_affiliation_strings":["School of Mathematics and Statistics, South\u2013Central University for Nationalities, Wuhan 430074, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, South\u2013Central University for Nationalities, Wuhan 430074, P. R. China","institution_ids":["https://openalex.org/I174442536"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5106414991"],"corresponding_institution_ids":["https://openalex.org/I158934434"],"apc_list":null,"apc_paid":null,"fwci":0.7483,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.71650212,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"23","issue":"01","first_page":"1350007","last_page":"1350007"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9987999796867371,"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":0.9987999796867371,"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":0.9973000288009644,"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"}},{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9945999979972839,"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/invariant","display_name":"Invariant (physics)","score":0.6889491081237793},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.67225581407547},{"id":"https://openalex.org/keywords/exponential-growth","display_name":"Exponential growth","score":0.662233293056488},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.5847480297088623},{"id":"https://openalex.org/keywords/chaotic-systems","display_name":"Chaotic systems","score":0.5630229711532593},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4500739872455597},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4430282711982727},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4419462978839874},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.41469722986221313},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24859529733657837},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22037094831466675},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.070187509059906},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.06378456950187683}],"concepts":[{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6889491081237793},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.67225581407547},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.662233293056488},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.5847480297088623},{"id":"https://openalex.org/C2987469083","wikidata":"https://www.wikidata.org/wiki/Q166314","display_name":"Chaotic systems","level":3,"score":0.5630229711532593},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4500739872455597},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4430282711982727},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4419462978839874},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.41469722986221313},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24859529733657837},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22037094831466675},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.070187509059906},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.06378456950187683},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127413500077","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127413500077","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1967008192","https://openalex.org/W1979959065","https://openalex.org/W1985725195","https://openalex.org/W1989604834","https://openalex.org/W1999534682","https://openalex.org/W2036845208","https://openalex.org/W2056473089","https://openalex.org/W2069436097","https://openalex.org/W2075523193","https://openalex.org/W2121020818","https://openalex.org/W2126098770","https://openalex.org/W2141394518","https://openalex.org/W2151223939","https://openalex.org/W2154488655","https://openalex.org/W2234683225","https://openalex.org/W2926309618"],"related_works":["https://openalex.org/W2804946780","https://openalex.org/W1991215068","https://openalex.org/W2740195320","https://openalex.org/W1968269471","https://openalex.org/W2378081698","https://openalex.org/W2003984024","https://openalex.org/W1997546313","https://openalex.org/W1984567683","https://openalex.org/W2036757540","https://openalex.org/W4240629575"],"abstract_inverted_index":{"In":[0],"this":[1,47,62],"paper,":[2],"the":[3,28,40],"existence":[4,29],"of":[5,14,30,39,46],"globally":[6,31],"exponentially":[7,32],"attractive":[8,33],"sets":[9,13],"and":[10,35],"positive":[11,36],"invariant":[12,37],"three-dimensional":[15],"autonomous":[16],"systems":[17],"with":[18],"only":[19],"cross-product":[20],"nonlinearities":[21],"are":[22,42],"considered.":[23],"Sufficient":[24],"conditions,":[25],"which":[26],"guarantee":[27],"set":[34,38],"system,":[41],"obtained.":[43],"The":[44,58],"results":[45,53],"paper":[48,63],"comprise":[49],"some":[50],"existing":[51],"relative":[52],"as":[54],"in":[55,61],"special":[56],"cases.":[57],"approach":[59],"presented":[60],"can":[64],"be":[65],"applied":[66],"to":[67],"study":[68],"other":[69],"chaotic":[70],"systems.":[71]},"counts_by_year":[{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
