{"id":"https://openalex.org/W2346598424","doi":"https://doi.org/10.1142/s0218127416500693","title":"A Chaotic System with Different Shapes of Equilibria","display_name":"A Chaotic System with Different Shapes of Equilibria","publication_year":2016,"publication_date":"2016-04-01","ids":{"openalex":"https://openalex.org/W2346598424","doi":"https://doi.org/10.1142/s0218127416500693","mag":"2346598424"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127416500693","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416500693","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/A5029973339","display_name":"Viet\u2013Thanh Pham","orcid":"https://orcid.org/0000-0001-5151-9812"},"institutions":[{"id":"https://openalex.org/I94518387","display_name":"Hanoi University of Science and Technology","ror":"https://ror.org/04nyv3z04","country_code":"VN","type":"education","lineage":["https://openalex.org/I94518387"]}],"countries":["VN"],"is_corresponding":true,"raw_author_name":"Viet-Thanh Pham","raw_affiliation_strings":["School of Electronics and Telecommunications, Hanoi University of Science and Technology, 01 Dai Co Viet, Hanoi, Vietnam"],"affiliations":[{"raw_affiliation_string":"School of Electronics and Telecommunications, Hanoi University of Science and Technology, 01 Dai Co Viet, Hanoi, Vietnam","institution_ids":["https://openalex.org/I94518387"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014962078","display_name":"Sajad Jafari","orcid":"https://orcid.org/0000-0002-6845-7539"},"institutions":[{"id":"https://openalex.org/I158248296","display_name":"Amirkabir University of Technology","ror":"https://ror.org/04gzbav43","country_code":"IR","type":"education","lineage":["https://openalex.org/I158248296"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Sajad Jafari","raw_affiliation_strings":["Biomedical Engineering Department, Amirkabir University of Technology, Tehran 15875-4413, Iran"],"affiliations":[{"raw_affiliation_string":"Biomedical Engineering Department, Amirkabir University of Technology, Tehran 15875-4413, Iran","institution_ids":["https://openalex.org/I158248296"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100359252","display_name":"Xiong Wang","orcid":"https://orcid.org/0000-0003-0211-1946"},"institutions":[{"id":"https://openalex.org/I180726961","display_name":"Shenzhen University","ror":"https://ror.org/01vy4gh70","country_code":"CN","type":"education","lineage":["https://openalex.org/I180726961"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiong Wang","raw_affiliation_strings":["Institute for Advanced Study, Shenzhen University, Shenzhen, Guangdong 518060, P. R. China"],"affiliations":[{"raw_affiliation_string":"Institute for Advanced Study, Shenzhen University, Shenzhen, Guangdong 518060, P. R. China","institution_ids":["https://openalex.org/I180726961"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100357282","display_name":"Jun Ma","orcid":"https://orcid.org/0000-0002-6127-000X"},"institutions":[{"id":"https://openalex.org/I22716506","display_name":"Lanzhou University of Technology","ror":"https://ror.org/03panb555","country_code":"CN","type":"education","lineage":["https://openalex.org/I22716506"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun Ma","raw_affiliation_strings":["Department of Physics, Lanzhou University of Technology, Lanzhou 730050, P. R. China"],"affiliations":[{"raw_affiliation_string":"Department of Physics, Lanzhou University of Technology, Lanzhou 730050, P. R. China","institution_ids":["https://openalex.org/I22716506"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5029973339"],"corresponding_institution_ids":["https://openalex.org/I94518387"],"apc_list":null,"apc_paid":null,"fwci":13.8914,"has_fulltext":false,"cited_by_count":96,"citation_normalized_percentile":{"value":0.99189878,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"26","issue":"04","first_page":"1650069","last_page":"1650069"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9990000128746033,"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":0.9990000128746033,"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":0.9944999814033508,"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":0.991100013256073,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.8962935209274292},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.8575718402862549},{"id":"https://openalex.org/keywords/chaotic-hysteresis","display_name":"Chaotic hysteresis","score":0.816911518573761},{"id":"https://openalex.org/keywords/crisis","display_name":"Crisis","score":0.7863231897354126},{"id":"https://openalex.org/keywords/r\u00f6ssler-attractor","display_name":"R\u00f6ssler attractor","score":0.7106647491455078},{"id":"https://openalex.org/keywords/rectangle","display_name":"Rectangle","score":0.6327374577522278},{"id":"https://openalex.org/keywords/ellipse","display_name":"Ellipse","score":0.6155126690864563},{"id":"https://openalex.org/keywords/equilibrium-point","display_name":"Equilibrium point","score":0.6122266054153442},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5125346183776855},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.42664068937301636},{"id":"https://openalex.org/keywords/synchronization-of-chaos","display_name":"Synchronization of chaos","score":0.29680174589157104},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29322460293769836},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2604370713233948},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2534255385398865},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.2279597520828247},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.20742300152778625},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19182008504867554},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.12418520450592041},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.09557041525840759}],"concepts":[{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.8962935209274292},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.8575718402862549},{"id":"https://openalex.org/C207219937","wikidata":"https://www.wikidata.org/wiki/Q5072841","display_name":"Chaotic hysteresis","level":5,"score":0.816911518573761},{"id":"https://openalex.org/C78302928","wikidata":"https://www.wikidata.org/wiki/Q5185947","display_name":"Crisis","level":4,"score":0.7863231897354126},{"id":"https://openalex.org/C192872217","wikidata":"https://www.wikidata.org/wiki/Q720574","display_name":"R\u00f6ssler attractor","level":3,"score":0.7106647491455078},{"id":"https://openalex.org/C2781302577","wikidata":"https://www.wikidata.org/wiki/Q209","display_name":"Rectangle","level":2,"score":0.6327374577522278},{"id":"https://openalex.org/C74261601","wikidata":"https://www.wikidata.org/wiki/Q40112","display_name":"Ellipse","level":2,"score":0.6155126690864563},{"id":"https://openalex.org/C94766913","wikidata":"https://www.wikidata.org/wiki/Q1530271","display_name":"Equilibrium point","level":3,"score":0.6122266054153442},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5125346183776855},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.42664068937301636},{"id":"https://openalex.org/C202759130","wikidata":"https://www.wikidata.org/wiki/Q7662148","display_name":"Synchronization of chaos","level":4,"score":0.29680174589157104},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29322460293769836},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2604370713233948},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2534255385398865},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.2279597520828247},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.20742300152778625},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19182008504867554},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.12418520450592041},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.09557041525840759},{"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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"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/s0218127416500693","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416500693","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":[{"id":"https://openalex.org/F4320309617","display_name":"National Foundation for Science and Technology Development","ror":"https://ror.org/04rw64z44"},{"id":"https://openalex.org/F4320309893","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23"},{"id":"https://openalex.org/F4320322170","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W242476103","https://openalex.org/W1464403884","https://openalex.org/W1967008192","https://openalex.org/W1967332757","https://openalex.org/W1972634840","https://openalex.org/W1990987436","https://openalex.org/W2028482099","https://openalex.org/W2029570895","https://openalex.org/W2032125478","https://openalex.org/W2040069863","https://openalex.org/W2048765588","https://openalex.org/W2069436097","https://openalex.org/W2127445253","https://openalex.org/W2140954225","https://openalex.org/W2141394518","https://openalex.org/W2141662965","https://openalex.org/W2152254020","https://openalex.org/W2164315701","https://openalex.org/W2169982364","https://openalex.org/W2964079314","https://openalex.org/W4247794243"],"related_works":["https://openalex.org/W2346598424","https://openalex.org/W2070724789","https://openalex.org/W2354020126","https://openalex.org/W3048874476","https://openalex.org/W2094388062","https://openalex.org/W2055644003","https://openalex.org/W2962792453","https://openalex.org/W1999265438","https://openalex.org/W2001163940","https://openalex.org/W2410336490"],"abstract_inverted_index":{"Although":[0],"many":[1],"chaotic":[2,33,50,55,60,66],"systems":[3,34],"have":[4],"been":[5],"introduced":[6],"in":[7],"the":[8,28,32],"literature,":[9],"a":[10],"few":[11],"of":[12,21,31,39],"them":[13],"possess":[14],"uncountably":[15],"infinite":[16,37],"equilibrium":[17],"points.":[18],"The":[19],"aim":[20],"our":[22],"short":[23],"work":[24],"is":[25,71],"to":[26],"widen":[27],"current":[29],"knowledge":[30],"with":[35,44,52,57,62,68],"an":[36],"number":[38],"equilibria.":[40],"A":[41],"three-dimensional":[42],"system":[43],"special":[45],"properties,":[46],"for":[47],"example,":[48],"exhibiting":[49],"attractor":[51,56,61,67],"circular":[53],"equilibrium,":[54,59,64,70],"ellipse":[58],"square-shaped":[63],"and":[65],"rectangle-shaped":[69],"proposed.":[72]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":14},{"year":2019,"cited_by_count":14},{"year":2018,"cited_by_count":22},{"year":2017,"cited_by_count":22},{"year":2016,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}