{"id":"https://openalex.org/W2003984024","doi":"https://doi.org/10.1155/2013/590421","title":"A New Series of Three-Dimensional Chaotic Systems with Cross-Product Nonlinearities and Their Switching","display_name":"A New Series of Three-Dimensional Chaotic Systems with Cross-Product Nonlinearities and Their Switching","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2003984024","doi":"https://doi.org/10.1155/2013/590421","mag":"2003984024"},"language":"en","primary_location":{"id":"doi:10.1155/2013/590421","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/590421","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/590421.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2013/590421.pdf","any_repository_has_fulltext":true},"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, China"],"affiliations":[{"raw_affiliation_string":"School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, 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, China"],"affiliations":[{"raw_affiliation_string":"School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, China","institution_ids":["https://openalex.org/I158934434"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100374006","display_name":"Zhigang Zhang","orcid":"https://orcid.org/0009-0004-9603-1641"},"institutions":[{"id":"https://openalex.org/I4210099437","display_name":"Hubei University Of Economics","ror":"https://ror.org/012a84b59","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210099437"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhigang Zhang","raw_affiliation_strings":["Department of Statistics and Applied Mathematics, Hubei University of Economics, Wuhan 430205, China"],"affiliations":[{"raw_affiliation_string":"Department of Statistics and Applied Mathematics, Hubei University of Economics, Wuhan 430205, China","institution_ids":["https://openalex.org/I4210099437"]}]},{"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-Central University for Nationalities, Wuhan 430074, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, South-Central University for Nationalities, Wuhan 430074, China","institution_ids":["https://openalex.org/I174442536"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5106414991"],"corresponding_institution_ids":["https://openalex.org/I158934434"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.7479,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.71316709,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"2013","issue":null,"first_page":"1","last_page":"14"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9986000061035156,"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":0.9986000061035156,"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":0.9976000189781189,"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":0.9955000281333923,"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/chaotic","display_name":"Chaotic","score":0.7936459183692932},{"id":"https://openalex.org/keywords/chaotic-systems","display_name":"Chaotic systems","score":0.6830291748046875},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5995073318481445},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5843918323516846},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5429101586341858},{"id":"https://openalex.org/keywords/exponential-growth","display_name":"Exponential growth","score":0.5400112867355347},{"id":"https://openalex.org/keywords/cross-product","display_name":"Cross product","score":0.5366975665092468},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5078690648078918},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48892512917518616},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4849731922149658},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4628125727176666},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.40195026993751526},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3920317590236664},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15227657556533813},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06232538819313049},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.056704819202423096}],"concepts":[{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.7936459183692932},{"id":"https://openalex.org/C2987469083","wikidata":"https://www.wikidata.org/wiki/Q166314","display_name":"Chaotic systems","level":3,"score":0.6830291748046875},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5995073318481445},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5843918323516846},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5429101586341858},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.5400112867355347},{"id":"https://openalex.org/C82927061","wikidata":"https://www.wikidata.org/wiki/Q178192","display_name":"Cross product","level":2,"score":0.5366975665092468},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5078690648078918},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48892512917518616},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4849731922149658},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4628125727176666},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.40195026993751526},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3920317590236664},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15227657556533813},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06232538819313049},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.056704819202423096},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2013/590421","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/590421","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/590421.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1394807632","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jam/1394807632","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:590421","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2013/590421.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:9b668a52e3fe45d5aed5c7a80dec71c8","is_oa":true,"landing_page_url":"https://doaj.org/article/9b668a52e3fe45d5aed5c7a80dec71c8","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2013 (2013)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2013/590421","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/590421","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/590421.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1231421488","display_name":null,"funder_award_id":"under","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2082826544","display_name":null,"funder_award_id":"Postdoctoral","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G21377279","display_name":null,"funder_award_id":"2012M511615","funder_id":"https://openalex.org/F4320322186","funder_display_name":"Natural Science Foundation of Hubei Province"},{"id":"https://openalex.org/G2376276132","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G2703358390","display_name":null,"funder_award_id":"60474011","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2936231424","display_name":null,"funder_award_id":"2009CDB026","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G3185904233","display_name":null,"funder_award_id":"60904005","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G3279335340","display_name":null,"funder_award_id":"2009CDB026","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3306903477","display_name":null,"funder_award_id":"2012M511615","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4932287013","display_name":null,"funder_award_id":"60904005","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5469106741","display_name":null,"funder_award_id":"2012M","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7033253288","display_name":null,"funder_award_id":"Grants","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7355953785","display_name":null,"funder_award_id":"60474011","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G7551403257","display_name":null,"funder_award_id":"2012M511615","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G766446384","display_name":null,"funder_award_id":"2012M511615","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G8208342437","display_name":null,"funder_award_id":"1 and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8951484681","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"},{"id":"https://openalex.org/F4320322186","display_name":"Natural Science Foundation of Hubei Province","ror":null},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2003984024.pdf","grobid_xml":"https://content.openalex.org/works/W2003984024.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W117662906","https://openalex.org/W1967008192","https://openalex.org/W1985725195","https://openalex.org/W1994859578","https://openalex.org/W1995378634","https://openalex.org/W1999534682","https://openalex.org/W2018874482","https://openalex.org/W2035270688","https://openalex.org/W2036009506","https://openalex.org/W2036845208","https://openalex.org/W2043122468","https://openalex.org/W2052610693","https://openalex.org/W2058593714","https://openalex.org/W2061016947","https://openalex.org/W2069436097","https://openalex.org/W2075523193","https://openalex.org/W2075980089","https://openalex.org/W2096842173","https://openalex.org/W2126098770","https://openalex.org/W2141394518","https://openalex.org/W2151223939","https://openalex.org/W2154488655","https://openalex.org/W3021722416"],"related_works":["https://openalex.org/W1634993130","https://openalex.org/W1602624896","https://openalex.org/W2068371111","https://openalex.org/W32300376","https://openalex.org/W1519862060","https://openalex.org/W1974979356","https://openalex.org/W2353662484","https://openalex.org/W2084061773","https://openalex.org/W2794917831","https://openalex.org/W2104564563"],"abstract_inverted_index":{"This":[0],"paper":[1],"introduces":[2],"a":[3],"new":[4],"series":[5],"of":[6,32],"three-dimensional":[7,57],"chaotic":[8,34,58],"systems":[9,59],"with":[10,60],"cross-product":[11,61],"nonlinearities.":[12],"Based":[13],"on":[14],"some":[15,39,56],"conditions,":[16],"we":[17,37,54],"analyze":[18],"the":[19,47,65],"globally":[20,23],"exponentially":[21,25],"or":[22],"conditional":[24],"attractive":[26],"set":[27,31],"and":[28,46,63],"positive":[29],"invariant":[30],"these":[33],"systems.":[35],"Moreover,":[36],"give":[38],"known":[40],"examples":[41],"to":[42],"show":[43],"our":[44],"results,":[45],"exponential":[48],"estimation":[49],"is":[50],"explicitly":[51],"derived.":[52],"Finally,":[53],"construct":[55],"nonlinearities":[62],"study":[64],"switching":[66],"system":[67],"between":[68],"them.":[69]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-13T07:58:08.660418","created_date":"2025-10-10T00:00:00"}