{"id":"https://openalex.org/W3048823364","doi":"https://doi.org/10.1109/access.2020.3015865","title":"Bounded Orbits and Multiple Scroll Coexisting Attractors in a Dual System of Chua System","display_name":"Bounded Orbits and Multiple Scroll Coexisting Attractors in a Dual System of Chua System","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3048823364","doi":"https://doi.org/10.1109/access.2020.3015865","mag":"3048823364"},"language":"en","primary_location":{"id":"doi:10.1109/access.2020.3015865","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.3015865","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/09164970.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/09164970.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100320108","display_name":"Yue Liu","orcid":"https://orcid.org/0000-0003-1021-8970"},"institutions":[{"id":"https://openalex.org/I177877127","display_name":"The University of Western Australia","ror":"https://ror.org/047272k79","country_code":"AU","type":"education","lineage":["https://openalex.org/I177877127"]},{"id":"https://openalex.org/I4385474403","display_name":"Changchun University of Technology","ror":"https://ror.org/052pakb34","country_code":"CN","type":"education","lineage":["https://openalex.org/I4385474403"]}],"countries":["AU","CN"],"is_corresponding":false,"raw_author_name":"Yue Liu","raw_affiliation_strings":["College of Electrical and Electronic Engineering, Changchun University of Technology, Changchun, China","School of Electrical, Electronic and Computer Engineering, The University of Western Australia, Perth, Australia"],"raw_orcid":"https://orcid.org/0000-0003-1021-8970","affiliations":[{"raw_affiliation_string":"College of Electrical and Electronic Engineering, Changchun University of Technology, Changchun, China","institution_ids":["https://openalex.org/I4385474403"]},{"raw_affiliation_string":"School of Electrical, Electronic and Computer Engineering, The University of Western Australia, Perth, Australia","institution_ids":["https://openalex.org/I177877127"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017703480","display_name":"Herbert Ho\u2010Ching Iu","orcid":"https://orcid.org/0000-0002-0687-4038"},"institutions":[{"id":"https://openalex.org/I177877127","display_name":"The University of Western Australia","ror":"https://ror.org/047272k79","country_code":"AU","type":"education","lineage":["https://openalex.org/I177877127"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Herbert Ho-Ching Iu","raw_affiliation_strings":["School of Electrical, Electronic and Computer Engineering, The University of Western Australia, Perth, WA, Australia"],"raw_orcid":"https://orcid.org/0000-0002-0687-4038","affiliations":[{"raw_affiliation_string":"School of Electrical, Electronic and Computer Engineering, The University of Western Australia, Perth, WA, Australia","institution_ids":["https://openalex.org/I177877127"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100686747","display_name":"Hui Li","orcid":"https://orcid.org/0000-0002-5275-2226"},"institutions":[{"id":"https://openalex.org/I4385474403","display_name":"Changchun University of Technology","ror":"https://ror.org/052pakb34","country_code":"CN","type":"education","lineage":["https://openalex.org/I4385474403"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hui Li","raw_affiliation_strings":["College of Electrical and Electronic Engineering, Changchun University of Technology, Changchun, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Electrical and Electronic Engineering, Changchun University of Technology, Changchun, China","institution_ids":["https://openalex.org/I4385474403"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100402640","display_name":"Xuefeng Zhang","orcid":"https://orcid.org/0000-0002-2831-5747"},"institutions":[{"id":"https://openalex.org/I4385474403","display_name":"Changchun University of Technology","ror":"https://ror.org/052pakb34","country_code":"CN","type":"education","lineage":["https://openalex.org/I4385474403"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xuefeng Zhang","raw_affiliation_strings":["College of Electrical and Electronic Engineering, Changchun University of Technology, Changchun, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Electrical and Electronic Engineering, Changchun University of Technology, Changchun, China","institution_ids":["https://openalex.org/I4385474403"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":0.7001,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.67063611,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"8","issue":null,"first_page":"147907","last_page":"147918"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9988999962806702,"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":0.9988999962806702,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9933000206947327,"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/notation","display_name":"Notation","score":0.5621302723884583},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43964749574661255},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3807344436645508},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3718581199645996},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33180275559425354},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.25854751467704773},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.15766769647598267}],"concepts":[{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.5621302723884583},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43964749574661255},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3807344436645508},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3718581199645996},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33180275559425354},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.25854751467704773},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.15766769647598267}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/access.2020.3015865","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.3015865","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/09164970.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:openaire/41177cf4-2144-48f8-8036-1783b55c9ac6","is_oa":true,"landing_page_url":"https://admin.research-repository.uwa.edu.au/en/publications/41177cf4-2144-48f8-8036-1783b55c9ac6","pdf_url":null,"source":{"id":"https://openalex.org/S4306402523","display_name":"UWA Profiles and Research Repository (University of Western Australia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I177877127","host_organization_name":"The University of Western Australia","host_organization_lineage":["https://openalex.org/I177877127"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Liu, Y, Iu, H H C, Li, H & Zhang, X 2020, 'Bounded Orbits and Multiple Scroll Coexisting Attractors in a Dual System of Chua System', IEEE Access, vol. 8, 9164970, pp. 147907-147918. https://doi.org/10.1109/ACCESS.2020.3015865","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:pure.atira.dk:publications/41177cf4-2144-48f8-8036-1783b55c9ac6","is_oa":true,"landing_page_url":"https://research-repository.uwa.edu.au/en/publications/41177cf4-2144-48f8-8036-1783b55c9ac6","pdf_url":null,"source":{"id":"https://openalex.org/S4306402523","display_name":"UWA Profiles and Research Repository (University of Western Australia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I177877127","host_organization_name":"The University of Western Australia","host_organization_lineage":["https://openalex.org/I177877127"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Liu, Y, Iu, H H C, Li, H & Zhang, X 2020, 'Bounded Orbits and Multiple Scroll Coexisting Attractors in a Dual System of Chua System', IEEE Access, vol. 8, 9164970, pp. 147907-147918. https://doi.org/10.1109/ACCESS.2020.3015865","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:818f8a02e6464fbebd27687574b42eb1","is_oa":false,"landing_page_url":"https://doaj.org/article/818f8a02e6464fbebd27687574b42eb1","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access, Vol 8, Pp 147907-147918 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2020.3015865","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.3015865","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/09164970.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322725","display_name":"China Scholarship Council","ror":"https://ror.org/04atp4p48"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3048823364.pdf","grobid_xml":"https://content.openalex.org/works/W3048823364.grobid-xml"},"referenced_works_count":42,"referenced_works":["https://openalex.org/W1249165066","https://openalex.org/W1892177549","https://openalex.org/W1981938824","https://openalex.org/W1998942494","https://openalex.org/W2025740212","https://openalex.org/W2037060484","https://openalex.org/W2086526964","https://openalex.org/W2167350925","https://openalex.org/W2205614439","https://openalex.org/W2215594976","https://openalex.org/W2229040072","https://openalex.org/W2249740901","https://openalex.org/W2460300317","https://openalex.org/W2471149905","https://openalex.org/W2488851856","https://openalex.org/W2499848935","https://openalex.org/W2523137896","https://openalex.org/W2542941274","https://openalex.org/W2549893486","https://openalex.org/W2576503728","https://openalex.org/W2588148365","https://openalex.org/W2614101859","https://openalex.org/W2634158718","https://openalex.org/W2768537761","https://openalex.org/W2779265082","https://openalex.org/W2780815966","https://openalex.org/W2801680959","https://openalex.org/W2883796729","https://openalex.org/W2892636303","https://openalex.org/W2914354021","https://openalex.org/W2915042284","https://openalex.org/W2917217396","https://openalex.org/W2918576491","https://openalex.org/W2960696614","https://openalex.org/W2963018423","https://openalex.org/W2979804996","https://openalex.org/W3018767337","https://openalex.org/W3025074292","https://openalex.org/W3035816212","https://openalex.org/W3100813589","https://openalex.org/W6722943042","https://openalex.org/W6785455678"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2051487156","https://openalex.org/W2504004674","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027"],"abstract_inverted_index":{"A":[0],"special":[1],"three-dimensional":[2],"chaotic":[3],"system":[4,12,44,62],"was":[5],"proposed":[6],"in":[7,118],"2016,":[8],"as":[9,139],"a":[10,81],"dual":[11],"of":[13,124,131,135,150,165],"Chua":[14,61],"system,":[15],"which":[16,193],"is":[17,112],"satisfied":[18],"<inline-formula":[19,26,46,53,64,71,88,98],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[20,27,34,47,54,65,72,86,89,96,99,106],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[21,28,48,55,66,73,90,100],"<tex-math":[22,29,49,56,67,74,91,101],"notation=\"LaTeX\">$a_{12}\\cdot":[23,50,68],"$":[24,51,69,93,103],"</tex-math></inline-formula>":[25,32,52,58,70,76,94,104],"notation=\"LaTeX\">$a_{21}&lt;":[30],"0$":[31],"<italic":[33,85,95,105],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">.</i>":[35],"The":[36],"dynamics":[37],"characteristics":[38],"are":[39,169,174,191,194],"different":[40],"from":[41],"the":[42,122,125,132,157,161,166,181,197],"Jerk":[43],"(":[45,63],"notation=\"LaTeX\">$a_{21}=0$":[57],")":[59],"and":[60,141,144,148,156,163,186,199],"notation=\"LaTeX\">$a_{21}&gt;0$":[75],").":[77],"In":[78],"this":[79,115],"paper,":[80],"method":[82],"for":[83,114,176],"generating":[84],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">M</i>":[87],"notation=\"LaTeX\">$\\times":[92,102],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">N</i>":[97],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">L</i>":[107],"grid":[108],"multiple":[109,187],"scroll":[110,167,188],"attractors":[111,168,190],"presented":[113],"system.":[116],"Also,":[117],"order":[119],"to":[120,196],"ensure":[121],"rigor":[123],"theoretical":[126],"results,":[127],"we":[128],"prove":[129],"existence":[130],"complex":[133],"scenario":[134],"bounded":[136,178],"orbits,":[137,143],"such":[138],"homoclinic":[140],"heteroclinic":[142],"illustrate":[145],"concurrent":[146],"created":[147],"annihilated":[149],"symmetric":[151],"orbits.":[152,179],"Then,":[153],"Shilnikov":[154],"bifurcation":[155,184],"possible":[158],"relationship":[159],"between":[160],"birth":[162],"death":[164],"studied.":[170],"Furthermore,":[171],"two":[172],"theorems":[173],"demonstrated":[175],"these":[177],"Finally,":[180],"Lyapunov":[182],"exponents,":[183],"diagrams,":[185],"coexisting":[189],"displayed,":[192],"related":[195],"parameters":[198],"initial":[200],"condition.":[201]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2020-08-18T00:00:00"}