{"id":"https://openalex.org/W3159244660","doi":"https://doi.org/10.1142/s0218127421300147","title":"Coexisting Infinite Equilibria and Chaos","display_name":"Coexisting Infinite Equilibria and Chaos","publication_year":2021,"publication_date":"2021-04-01","ids":{"openalex":"https://openalex.org/W3159244660","doi":"https://doi.org/10.1142/s0218127421300147","mag":"3159244660"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127421300147","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127421300147","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/I200845125","display_name":"Nanjing University of Information Science and Technology","ror":"https://ror.org/02y0rxk19","country_code":"CN","type":"education","lineage":["https://openalex.org/I200845125"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Chunbiao Li","raw_affiliation_strings":["Jiangsu Collaborative Innovation Center of Atmospheric, Environment and Equipment Technology (CICAEET), Nanjing University of Information Science and Technology, Nanjing 210044, P. R. China","School of Artificial Intelligence, Nanjing University of Information Science and Technology, Nanjing 210044, P. R. China"],"raw_orcid":"https://orcid.org/0000-0002-9932-0914","affiliations":[{"raw_affiliation_string":"Jiangsu Collaborative Innovation Center of Atmospheric, Environment and Equipment Technology (CICAEET), Nanjing University of Information Science and Technology, Nanjing 210044, P. R. China","institution_ids":["https://openalex.org/I200845125"]},{"raw_affiliation_string":"School of Artificial Intelligence, Nanjing University of Information Science and Technology, Nanjing 210044, P. R. China","institution_ids":["https://openalex.org/I200845125"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101434831","display_name":"Yuxuan Peng","orcid":"https://orcid.org/0000-0001-7874-1368"},"institutions":[{"id":"https://openalex.org/I200845125","display_name":"Nanjing University of Information Science and Technology","ror":"https://ror.org/02y0rxk19","country_code":"CN","type":"education","lineage":["https://openalex.org/I200845125"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuxuan Peng","raw_affiliation_strings":["Jiangsu Collaborative Innovation Center of Atmospheric, Environment and Equipment Technology (CICAEET), Nanjing University of Information Science and Technology, Nanjing 210044, P. R. China","Jiangsu Key Laboratory of Meteorological Observation and Information Processing, Nanjing University of Information, Science and Technology, Nanjing 210044, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Jiangsu Collaborative Innovation Center of Atmospheric, Environment and Equipment Technology (CICAEET), Nanjing University of Information Science and Technology, Nanjing 210044, P. R. China","institution_ids":["https://openalex.org/I200845125"]},{"raw_affiliation_string":"Jiangsu Key Laboratory of Meteorological Observation and Information Processing, Nanjing University of Information, Science and Technology, Nanjing 210044, P. R. China","institution_ids":["https://openalex.org/I200845125"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102973777","display_name":"Ze Tao","orcid":"https://orcid.org/0000-0003-4009-194X"},"institutions":[{"id":"https://openalex.org/I200845125","display_name":"Nanjing University of Information Science and Technology","ror":"https://ror.org/02y0rxk19","country_code":"CN","type":"education","lineage":["https://openalex.org/I200845125"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ze Tao","raw_affiliation_strings":["Jiangsu Collaborative Innovation Center of Atmospheric, Environment and Equipment Technology (CICAEET), Nanjing University of Information Science and Technology, Nanjing 210044, P. R. China","Jiangsu Key Laboratory of Meteorological Observation and Information Processing, Nanjing University of Information, Science and Technology, Nanjing 210044, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Jiangsu Collaborative Innovation Center of Atmospheric, Environment and Equipment Technology (CICAEET), Nanjing University of Information Science and Technology, Nanjing 210044, P. R. China","institution_ids":["https://openalex.org/I200845125"]},{"raw_affiliation_string":"Jiangsu Key Laboratory of Meteorological Observation and Information Processing, Nanjing University of Information, Science and Technology, Nanjing 210044, P. R. China","institution_ids":["https://openalex.org/I200845125"]}]},{"author_position":"middle","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":"Julien Clinton Sprott","raw_affiliation_strings":["Department of Physics, University of Wisconsin-Madison, Madison, WI 53706, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, University of Wisconsin-Madison, Madison, WI 53706, USA","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"last","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 Faculty, Amirkabir University of Technology, 424 Hafez Ave, 15875-4413, Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Biomedical Engineering Faculty, Amirkabir University of Technology, 424 Hafez Ave, 15875-4413, Tehran, Iran","institution_ids":["https://openalex.org/I158248296"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5031215480"],"corresponding_institution_ids":["https://openalex.org/I200845125"],"apc_list":null,"apc_paid":null,"fwci":4.7256,"has_fulltext":false,"cited_by_count":40,"citation_normalized_percentile":{"value":0.95818949,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"31","issue":"05","first_page":"2130014","last_page":"2130014"},"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":0.9973000288009644,"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":0.9950000047683716,"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":0.9012458324432373},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.7751610279083252},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.6913770437240601},{"id":"https://openalex.org/keywords/chaotic-hysteresis","display_name":"Chaotic hysteresis","score":0.5566803812980652},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5107021927833557},{"id":"https://openalex.org/keywords/synchronization-of-chaos","display_name":"Synchronization of chaos","score":0.5047005414962769},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49676209688186646},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.49282148480415344},{"id":"https://openalex.org/keywords/oscillation","display_name":"Oscillation (cell signaling)","score":0.4201262593269348},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.40608155727386475},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.26277992129325867},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2531593441963196},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2482641041278839},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.08804497122764587}],"concepts":[{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.9012458324432373},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.7751610279083252},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.6913770437240601},{"id":"https://openalex.org/C207219937","wikidata":"https://www.wikidata.org/wiki/Q5072841","display_name":"Chaotic hysteresis","level":5,"score":0.5566803812980652},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5107021927833557},{"id":"https://openalex.org/C202759130","wikidata":"https://www.wikidata.org/wiki/Q7662148","display_name":"Synchronization of chaos","level":4,"score":0.5047005414962769},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49676209688186646},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.49282148480415344},{"id":"https://openalex.org/C2778439541","wikidata":"https://www.wikidata.org/wiki/Q7106412","display_name":"Oscillation (cell signaling)","level":2,"score":0.4201262593269348},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.40608155727386475},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.26277992129325867},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2531593441963196},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2482641041278839},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.08804497122764587},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127421300147","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127421300147","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":[{"id":"https://openalex.org/G1993483461","display_name":null,"funder_award_id":"61871230","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4627539250","display_name":null,"funder_award_id":"61971228","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5889787216","display_name":null,"funder_award_id":"BK20181410","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322769","display_name":"Natural Science Foundation of Jiangsu Province","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320327518","display_name":"Priority Academic Program Development of Jiangsu Higher Education Institutions","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W101784450","https://openalex.org/W1656086158","https://openalex.org/W1968999011","https://openalex.org/W1972634840","https://openalex.org/W1973078866","https://openalex.org/W1998630995","https://openalex.org/W2040069863","https://openalex.org/W2054975916","https://openalex.org/W2061650609","https://openalex.org/W2067470760","https://openalex.org/W2083531786","https://openalex.org/W2119566600","https://openalex.org/W2127445253","https://openalex.org/W2134411482","https://openalex.org/W2141662965","https://openalex.org/W2143811734","https://openalex.org/W2164315701","https://openalex.org/W2169982364","https://openalex.org/W2176200890","https://openalex.org/W2293773556","https://openalex.org/W2468907312","https://openalex.org/W2490150532","https://openalex.org/W2496576690","https://openalex.org/W2528437065","https://openalex.org/W2542941274","https://openalex.org/W2604704152","https://openalex.org/W2634158718","https://openalex.org/W2746989737","https://openalex.org/W2762922087","https://openalex.org/W2770088462","https://openalex.org/W2797416178","https://openalex.org/W2909453129","https://openalex.org/W2914023782","https://openalex.org/W2943584482","https://openalex.org/W2964079314","https://openalex.org/W2971162636","https://openalex.org/W2972978930","https://openalex.org/W3100211151"],"related_works":["https://openalex.org/W2136889839","https://openalex.org/W2411553537","https://openalex.org/W2378640948","https://openalex.org/W1483423523","https://openalex.org/W3014531371","https://openalex.org/W2186829394","https://openalex.org/W2802455359","https://openalex.org/W3014978777","https://openalex.org/W2001163940","https://openalex.org/W3037847165"],"abstract_inverted_index":{"Equilibria":[0],"are":[1,76,84,158],"a":[2,11,23,92,142,153,177],"class":[3],"of":[4,16,33,82,114,119,149,156],"attractors":[5,30],"that":[6,91],"host":[7],"inherent":[8],"stability":[9],"in":[10,22,141],"dynamic":[12],"system.":[13,179],"Infinite":[14],"number":[15,148],"equilibria":[17,35,44,63,75,83,104,115,150,157],"and":[18,64,78],"chaos":[19],"sometimes":[20],"coexist":[21,52],"system":[24,94,135,164],"with":[25,53,72,123,184],"some":[26],"connections.":[27],"Hidden":[28],"chaotic":[29,55,65,70,88,93,121,163],"exist":[31],"independent":[32],"any":[34],"rather":[36],"than":[37],"being":[38],"excited":[39],"by":[40],"them.":[41],"However,":[42],"the":[43,54,59,62,87,101,108,117,120,134,162,167,185],"can":[45,95],"modify,":[46],"distort,":[47],"eliminate,":[48],"or":[49,131,151],"even":[50,139,152],"instead":[51],"attractor":[56],"depending":[57],"on":[58],"distance":[60],"between":[61],"attractor.":[66,110],"In":[67],"this":[68],"paper,":[69],"systems":[71],"infinitely":[73],"many":[74],"considered":[77],"explored.":[79],"Extra":[80],"surfaces":[81],"introduced":[85],"into":[86,136,161],"flows,":[89],"showing":[90],"maintain":[96],"its":[97],"basic":[98],"dynamics":[99],"if":[100],"newly":[102],"added":[103],"do":[105],"not":[106],"intersect":[107],"original":[109,168],"The":[111],"offset-boostable":[112],"plane":[113],"rescales":[116],"frequency":[118],"oscillation":[122],"an":[124,172],"almost":[125],"linearly":[126],"modified":[127],"largest":[128],"Lyapunov":[129],"exponent":[130],"conversely":[132],"drives":[133],"periodic":[137],"oscillation,":[138],"ending":[140],"divergent":[143],"state.":[144],"Furthermore,":[145],"additional":[146],"infinite":[147],"solid":[154],"space":[155],"safely":[159],"nested":[160],"without":[165],"destroying":[166],"dynamics,":[169],"which":[170],"provides":[171],"alternate":[173],"permanent":[174],"location":[175],"for":[176],"dynamical":[178],"A":[180],"circuit":[181],"simulation":[182],"agrees":[183],"numerical":[186],"calculation.":[187]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":15},{"year":2021,"cited_by_count":7}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}