{"id":"https://openalex.org/W4297042806","doi":"https://doi.org/10.1155/2022/6921934","title":"Stability, Chaos, and Bifurcation Analysis of a Discrete Chemical System","display_name":"Stability, Chaos, and Bifurcation Analysis of a Discrete Chemical System","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4297042806","doi":"https://doi.org/10.1155/2022/6921934"},"language":"en","primary_location":{"id":"doi:10.1155/2022/6921934","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/6921934","pdf_url":"https://downloads.hindawi.com/journals/complexity/2022/6921934.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/2022/6921934.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052541435","display_name":"Abdul Qadeer Khan","orcid":"https://orcid.org/0000-0002-0278-1352"},"institutions":[{"id":"https://openalex.org/I146840658","display_name":"University of Azad Jammu and Kashmir","ror":"https://ror.org/015566d55","country_code":"PK","type":"education","lineage":["https://openalex.org/I146840658"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Abdul Qadeer Khan","raw_affiliation_strings":["Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad 13100, Pakistan","Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad 13100"],"raw_orcid":"https://orcid.org/0000-0002-0278-1352","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad 13100, Pakistan","institution_ids":["https://openalex.org/I146840658"]},{"raw_affiliation_string":"Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad 13100","institution_ids":["https://openalex.org/I146840658"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032720419","display_name":"Ibraheem M. Alsulami","orcid":"https://orcid.org/0000-0002-2174-6915"},"institutions":[{"id":"https://openalex.org/I199693650","display_name":"Umm al-Qura University","ror":"https://ror.org/01xjqrm90","country_code":"SA","type":"education","lineage":["https://openalex.org/I199693650"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Ibraheem M. Alsulami","raw_affiliation_strings":["Department of Mathematical Science, Faculty of Applied Science, Umm Al-Qura University, Makkah 21955, Saudi Arabia","Department of Mathematical Science, Faculty of Applied Science, Umm Al-Qura University, Makkah 21955"],"raw_orcid":"https://orcid.org/0000-0002-2174-6915","affiliations":[{"raw_affiliation_string":"Department of Mathematical Science, Faculty of Applied Science, Umm Al-Qura University, Makkah 21955, Saudi Arabia","institution_ids":["https://openalex.org/I199693650"]},{"raw_affiliation_string":"Department of Mathematical Science, Faculty of Applied Science, Umm Al-Qura University, Makkah 21955","institution_ids":["https://openalex.org/I199693650"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000982316","display_name":"Umbreen Sadiq","orcid":null},"institutions":[{"id":"https://openalex.org/I146840658","display_name":"University of Azad Jammu and Kashmir","ror":"https://ror.org/015566d55","country_code":"PK","type":"education","lineage":["https://openalex.org/I146840658"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Umbreen Sadiq","raw_affiliation_strings":["Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad 13100, Pakistan","Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad 13100"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad 13100, Pakistan","institution_ids":["https://openalex.org/I146840658"]},{"raw_affiliation_string":"Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad 13100","institution_ids":["https://openalex.org/I146840658"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5052541435"],"corresponding_institution_ids":["https://openalex.org/I146840658"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":0.1426,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.49652778,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"2022","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9994000196456909,"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"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9969000220298767,"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9936000108718872,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/brusselator","display_name":"Brusselator","score":0.9421852827072144},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.4879126250743866},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47691604495048523},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.4235853850841522},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.39374080300331116},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.3795921802520752},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3756067156791687},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29083096981048584},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08908018469810486},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.06093612313270569}],"concepts":[{"id":"https://openalex.org/C14028793","wikidata":"https://www.wikidata.org/wiki/Q906505","display_name":"Brusselator","level":3,"score":0.9421852827072144},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.4879126250743866},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47691604495048523},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.4235853850841522},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.39374080300331116},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.3795921802520752},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3756067156791687},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29083096981048584},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08908018469810486},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.06093612313270569}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2022/6921934","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/6921934","pdf_url":"https://downloads.hindawi.com/journals/complexity/2022/6921934.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:6921934","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/complexity/2022/6921934.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:b779f10aa4aa4c79ac99f7dd8b6a396c","is_oa":false,"landing_page_url":"https://doaj.org/article/b779f10aa4aa4c79ac99f7dd8b6a396c","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":"Complexity, Vol 2022 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2022/6921934","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/6921934","pdf_url":"https://downloads.hindawi.com/journals/complexity/2022/6921934.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":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4297042806.pdf","grobid_xml":"https://content.openalex.org/works/W4297042806.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W126388413","https://openalex.org/W370471672","https://openalex.org/W1583357624","https://openalex.org/W1596321532","https://openalex.org/W1967704096","https://openalex.org/W1975210386","https://openalex.org/W1980161001","https://openalex.org/W1981573359","https://openalex.org/W2012394694","https://openalex.org/W2014626268","https://openalex.org/W2025904721","https://openalex.org/W2065705412","https://openalex.org/W2085252636","https://openalex.org/W2089876099","https://openalex.org/W2092688005","https://openalex.org/W2113839217","https://openalex.org/W2206613000","https://openalex.org/W2294043064","https://openalex.org/W2753992769","https://openalex.org/W2785155620","https://openalex.org/W2910997779","https://openalex.org/W2972732142","https://openalex.org/W2991520004","https://openalex.org/W3047318087","https://openalex.org/W3091243916","https://openalex.org/W3202648222","https://openalex.org/W4200337950","https://openalex.org/W4206642481","https://openalex.org/W4255777804"],"related_works":["https://openalex.org/W3139962778","https://openalex.org/W4293118301","https://openalex.org/W2907476374","https://openalex.org/W2390864159","https://openalex.org/W4386096380","https://openalex.org/W3153636207","https://openalex.org/W2352047479","https://openalex.org/W2069804810","https://openalex.org/W2291372883","https://openalex.org/W1997555467"],"abstract_inverted_index":{"The":[0,65,117],"local":[1,39],"dynamics,":[2],"chaos,":[3],"and":[4,77,86,114],"bifurcations":[5,68,88],"of":[6,60,67],"a":[7,17],"discrete":[8,18,55,81,132],"Brusselator":[9,19,56,82,133],"system":[10,20],"are":[11,42,138],"investigated.":[12,64],"It":[13],"is":[14,63,74,122],"shown":[15],"that":[16,79,128],"has":[21],"an":[22,70],"interior":[23,45,71],"fixed":[24,46,72],"point":[25,47,73],"P":[26,48,98],"(1,":[27,49,99],"r":[28,31,50,91,100,104,112],")":[29,94,101],"if":[30,89],">":[32],"0.":[33],"Then,":[34],"by":[35],"linear":[36],"stability":[37],"theory,":[38],"dynamical":[40],"characteristics":[41],"explored":[43],"at":[44],").":[51],"Furthermore,":[52],"for":[53],"the":[54,58,80,126,131],"system,":[57],"existence":[59,66],"periodic":[61],"points":[62],"around":[69],"also":[75],"investigated":[76],"proved":[78],"model":[83],"undergoes":[84],"hopf":[85],"flip":[87],"(":[90],",":[92,105,115],"h":[93,106,108],"\u2208":[95],"\u210b\u212c":[96],"|":[97],"=":[102,109],"{(":[103],"),":[107],"2":[110],"\u2212":[111],"}":[113],"respectively.":[116],"next":[118],"feedback":[119],"control":[120],"method":[121],"utilized":[123],"to":[124],"stabilize":[125],"chaos":[127],"exists":[129],"in":[130],"system.":[134],"Finally,":[135],"obtained":[136],"results":[137],"verified":[139],"numerically.":[140]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}