{"id":"https://openalex.org/W3193962579","doi":"https://doi.org/10.1155/2021/9948488","title":"Dynamical Analysis and Periodic Solution of a Chaotic System with Coexisting Attractors","display_name":"Dynamical Analysis and Periodic Solution of a Chaotic System with Coexisting Attractors","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3193962579","doi":"https://doi.org/10.1155/2021/9948488","mag":"3193962579"},"language":"en","primary_location":{"id":"doi:10.1155/2021/9948488","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2021/9948488","pdf_url":"https://downloads.hindawi.com/journals/complexity/2021/9948488.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"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":"Complexity","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/complexity/2021/9948488.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101784591","display_name":"Mingshu Chen","orcid":"https://orcid.org/0000-0002-3670-1680"},"institutions":[{"id":"https://openalex.org/I4210162994","display_name":"Xijing University","ror":"https://ror.org/05xsjkb63","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210162994"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Mingshu Chen","raw_affiliation_strings":["Shaanxi International Joint Research Center for Applied Technology of Controllable Neutron Source School of Science, Xijing University, Xi\u2019an 710123, China xijing.com.cn","Shaanxi International Joint Research Center for Applied Technology of Controllable Neutron Source School of Science, Xijing University, Xi'an 710123, China"],"raw_orcid":"https://orcid.org/0000-0002-3670-1680","affiliations":[{"raw_affiliation_string":"Shaanxi International Joint Research Center for Applied Technology of Controllable Neutron Source School of Science, Xijing University, Xi\u2019an 710123, China xijing.com.cn","institution_ids":["https://openalex.org/I4210162994"]},{"raw_affiliation_string":"Shaanxi International Joint Research Center for Applied Technology of Controllable Neutron Source School of Science, Xijing University, Xi'an 710123, China","institution_ids":["https://openalex.org/I4210162994"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100722361","display_name":"Zhen Wang","orcid":"https://orcid.org/0000-0002-9182-4421"},"institutions":[{"id":"https://openalex.org/I4210162994","display_name":"Xijing University","ror":"https://ror.org/05xsjkb63","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210162994"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhen Wang","raw_affiliation_strings":["Shaanxi International Joint Research Center for Applied Technology of Controllable Neutron Source School of Science, Xijing University, Xi\u2019an 710123, China xijing.com.cn","Shaanxi International Joint Research Center for Applied Technology of Controllable Neutron Source School of Science, Xijing University, Xi'an 710123, China"],"raw_orcid":"https://orcid.org/0000-0002-9182-4421","affiliations":[{"raw_affiliation_string":"Shaanxi International Joint Research Center for Applied Technology of Controllable Neutron Source School of Science, Xijing University, Xi\u2019an 710123, China xijing.com.cn","institution_ids":["https://openalex.org/I4210162994"]},{"raw_affiliation_string":"Shaanxi International Joint Research Center for Applied Technology of Controllable Neutron Source School of Science, Xijing University, Xi'an 710123, China","institution_ids":["https://openalex.org/I4210162994"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100457265","display_name":"Xiaojuan Zhang","orcid":"https://orcid.org/0000-0002-9932-3939"},"institutions":[{"id":"https://openalex.org/I4210162994","display_name":"Xijing University","ror":"https://ror.org/05xsjkb63","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210162994"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaojuan Zhang","raw_affiliation_strings":["Shaanxi International Joint Research Center for Applied Technology of Controllable Neutron Source School of Science, Xijing University, Xi\u2019an 710123, China xijing.com.cn","Shaanxi International Joint Research Center for Applied Technology of Controllable Neutron Source School of Science, Xijing University, Xi'an 710123, China"],"raw_orcid":"https://orcid.org/0000-0002-9932-3939","affiliations":[{"raw_affiliation_string":"Shaanxi International Joint Research Center for Applied Technology of Controllable Neutron Source School of Science, Xijing University, Xi\u2019an 710123, China xijing.com.cn","institution_ids":["https://openalex.org/I4210162994"]},{"raw_affiliation_string":"Shaanxi International Joint Research Center for Applied Technology of Controllable Neutron Source School of Science, Xijing University, Xi'an 710123, China","institution_ids":["https://openalex.org/I4210162994"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079974163","display_name":"Huaigu Tian","orcid":"https://orcid.org/0000-0003-3035-3555"},"institutions":[{"id":"https://openalex.org/I4210162994","display_name":"Xijing University","ror":"https://ror.org/05xsjkb63","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210162994"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huaigu Tian","raw_affiliation_strings":["Shaanxi International Joint Research Center for Applied Technology of Controllable Neutron Source School of Science, Xijing University, Xi\u2019an 710123, China xijing.com.cn","Shaanxi International Joint Research Center for Applied Technology of Controllable Neutron Source School of Science, Xijing University, Xi'an 710123, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shaanxi International Joint Research Center for Applied Technology of Controllable Neutron Source School of Science, Xijing University, Xi\u2019an 710123, China xijing.com.cn","institution_ids":["https://openalex.org/I4210162994"]},{"raw_affiliation_string":"Shaanxi International Joint Research Center for Applied Technology of Controllable Neutron Source School of Science, Xijing University, Xi'an 710123, China","institution_ids":["https://openalex.org/I4210162994"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5100722361"],"corresponding_institution_ids":["https://openalex.org/I4210162994"],"apc_list":{"value":2550,"currency":"USD","value_usd":2550},"apc_paid":{"value":2550,"currency":"USD","value_usd":2550},"fwci":0.1162,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.42182857,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"2021","issue":"1","first_page":null,"last_page":null},"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9993000030517578,"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":0.9976000189781189,"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/attractor","display_name":"Attractor","score":0.8084560632705688},{"id":"https://openalex.org/keywords/quasiperiodic-function","display_name":"Quasiperiodic function","score":0.6415813565254211},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.6090971231460571},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5924989581108093},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.5879842042922974},{"id":"https://openalex.org/keywords/poincar\u00e9-conjecture","display_name":"Poincar\u00e9 conjecture","score":0.5180420875549316},{"id":"https://openalex.org/keywords/instability","display_name":"Instability","score":0.49357855319976807},{"id":"https://openalex.org/keywords/computer-assisted-proof","display_name":"Computer-assisted proof","score":0.4639883041381836},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.43875396251678467},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.42333558201789856},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4195680618286133},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4083915054798126},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23672881722450256},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2193233072757721},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13754874467849731},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.05986371636390686}],"concepts":[{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.8084560632705688},{"id":"https://openalex.org/C55637507","wikidata":"https://www.wikidata.org/wiki/Q5870963","display_name":"Quasiperiodic function","level":2,"score":0.6415813565254211},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.6090971231460571},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5924989581108093},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.5879842042922974},{"id":"https://openalex.org/C88221313","wikidata":"https://www.wikidata.org/wiki/Q203586","display_name":"Poincar\u00e9 conjecture","level":2,"score":0.5180420875549316},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.49357855319976807},{"id":"https://openalex.org/C173613240","wikidata":"https://www.wikidata.org/wiki/Q1150675","display_name":"Computer-assisted proof","level":3,"score":0.4639883041381836},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.43875396251678467},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.42333558201789856},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4195680618286133},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4083915054798126},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23672881722450256},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2193233072757721},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13754874467849731},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.05986371636390686},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","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":3,"locations":[{"id":"doi:10.1155/2021/9948488","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2021/9948488","pdf_url":"https://downloads.hindawi.com/journals/complexity/2021/9948488.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"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":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:complx:9948488","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/complexity/2021/9948488.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:15cbd1e088084ca0a105c69b2b0b19a8","is_oa":true,"landing_page_url":"https://doaj.org/article/15cbd1e088084ca0a105c69b2b0b19a8","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Complexity, Vol 2021 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2021/9948488","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2021/9948488","pdf_url":"https://downloads.hindawi.com/journals/complexity/2021/9948488.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"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":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2889118353","display_name":null,"funder_award_id":"2020JM-646","funder_id":"https://openalex.org/F4320329602","funder_display_name":"Xijing University"},{"id":"https://openalex.org/G424435434","display_name":null,"funder_award_id":"2018GHJD-21","funder_id":"https://openalex.org/F4320329602","funder_display_name":"Xijing University"},{"id":"https://openalex.org/G6309084123","display_name":null,"funder_award_id":"2021JM-533","funder_id":"https://openalex.org/F4320329602","funder_display_name":"Xijing University"},{"id":"https://openalex.org/G8129564360","display_name":null,"funder_award_id":"2019218414GXRC020CG021-GXYD20.3","funder_id":"https://openalex.org/F4320329602","funder_display_name":"Xijing University"},{"id":"https://openalex.org/G8839430397","display_name":null,"funder_award_id":"2021JQ-880","funder_id":"https://openalex.org/F4320329602","funder_display_name":"Xijing University"}],"funders":[{"id":"https://openalex.org/F4320329602","display_name":"Xijing University","ror":"https://ror.org/05xsjkb63"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3193962579.pdf","grobid_xml":"https://content.openalex.org/works/W3193962579.grobid-xml"},"referenced_works_count":52,"referenced_works":["https://openalex.org/W101784450","https://openalex.org/W1515307033","https://openalex.org/W1967332757","https://openalex.org/W1990987436","https://openalex.org/W2005241888","https://openalex.org/W2036009506","https://openalex.org/W2036870441","https://openalex.org/W2041627097","https://openalex.org/W2049576731","https://openalex.org/W2069436097","https://openalex.org/W2083531786","https://openalex.org/W2087286123","https://openalex.org/W2092675093","https://openalex.org/W2093771333","https://openalex.org/W2096452248","https://openalex.org/W2101221046","https://openalex.org/W2141394518","https://openalex.org/W2147765123","https://openalex.org/W2225216977","https://openalex.org/W2398272915","https://openalex.org/W2494614581","https://openalex.org/W2496576690","https://openalex.org/W2624618313","https://openalex.org/W2760188900","https://openalex.org/W2762325369","https://openalex.org/W2770088462","https://openalex.org/W2780853794","https://openalex.org/W2792026505","https://openalex.org/W2795137742","https://openalex.org/W2797416178","https://openalex.org/W2807503488","https://openalex.org/W2883796729","https://openalex.org/W2894204232","https://openalex.org/W2943584482","https://openalex.org/W2963175336","https://openalex.org/W2964079314","https://openalex.org/W2972336707","https://openalex.org/W2980621048","https://openalex.org/W2990824185","https://openalex.org/W3010028395","https://openalex.org/W3022677734","https://openalex.org/W3022699902","https://openalex.org/W3025074292","https://openalex.org/W3036823495","https://openalex.org/W3048968476","https://openalex.org/W3100211151","https://openalex.org/W3101573852","https://openalex.org/W3112533795","https://openalex.org/W3118317596","https://openalex.org/W3119549848","https://openalex.org/W3125342352","https://openalex.org/W3127459604"],"related_works":["https://openalex.org/W3112195757","https://openalex.org/W3206287350","https://openalex.org/W4391047362","https://openalex.org/W1983278479","https://openalex.org/W2090194301","https://openalex.org/W4245819605","https://openalex.org/W2291648028","https://openalex.org/W2064725493","https://openalex.org/W2084127152","https://openalex.org/W2859951168"],"abstract_inverted_index":{"Chaotic":[0],"attractors":[1,32],"with":[2,5,10],"no":[3],"equilibria,":[4],"an":[6],"unstable":[7],"node,":[8],"and":[9,26,35],"stable":[11],"node\u2010focus":[12],"are":[13,21,33,54,76],"presented":[14],"in":[15,63],"this":[16,50],"paper.":[17],"The":[18,87],"conservative":[19],"solutions":[20],"investigated":[22],"by":[23,78],"the":[24,42,68,71,74,80,91],"semianalytical":[25],"seminumerical":[27],"method.":[28],"Furthermore,":[29],"multiple":[30],"coexisting":[31],"investigated,":[34],"circuit":[36],"is":[37],"carried":[38],"out.":[39],"To":[40],"study":[41],"system\u2019s":[43,81],"global":[44],"structure,":[45],"dynamics":[46,69],"at":[47],"infinity":[48,72],"for":[49],"new":[51],"chaotic":[52],"system":[53],"studied":[55],"using":[56],"Poincar\u00e9":[57,85],"compactification":[58],"of":[59,73],"polynomial":[60],"vector":[61],"fields":[62],"R":[64],"3":[65],".":[66],"Meanwhile,":[67],"near":[70],"singularities":[75],"obtained":[77],"reducing":[79],"dimensions":[82],"on":[83],"a":[84],"ball.":[86],"averaging":[88],"theory":[89],"analyzes":[90],"periodic":[92],"solution\u2019s":[93],"stability":[94],"or":[95],"instability":[96],"that":[97],"bifurcates":[98],"from":[99],"Hopf\u2010zero":[100],"bifurcation.":[101]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
