{"id":"https://openalex.org/W4407141748","doi":"https://doi.org/10.3390/axioms14020118","title":"On the Global Dynamics of a Fourth-Order Riccati-Type Exponential Fuzzy Difference Equation","display_name":"On the Global Dynamics of a Fourth-Order Riccati-Type Exponential Fuzzy Difference Equation","publication_year":2025,"publication_date":"2025-02-04","ids":{"openalex":"https://openalex.org/W4407141748","doi":"https://doi.org/10.3390/axioms14020118"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14020118","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14020118","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/axioms14020118","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008596168","display_name":"Asifa Tassaddiq","orcid":"https://orcid.org/0000-0002-6165-8055"},"institutions":[{"id":"https://openalex.org/I195631090","display_name":"Majmaah University","ror":"https://ror.org/01mcrnj60","country_code":"SA","type":"education","lineage":["https://openalex.org/I195631090"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Asifa Tassaddiq","raw_affiliation_strings":["Department of Computer Science, College of Computer and Information Sciences, Majmaah University, Al Majmaah 11952, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-6165-8055","affiliations":[{"raw_affiliation_string":"Department of Computer Science, College of Computer and Information Sciences, Majmaah University, Al Majmaah 11952, Saudi Arabia","institution_ids":["https://openalex.org/I195631090"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100731081","display_name":"Muhammad Tanveer","orcid":"https://orcid.org/0000-0002-3118-571X"},"institutions":[{"id":"https://openalex.org/I4210147796","display_name":"University of Faisalabad","ror":"https://ror.org/04eps4h65","country_code":"PK","type":"education","lineage":["https://openalex.org/I4210147796"]},{"id":"https://openalex.org/I61623833","display_name":"University of Agriculture Faisalabad","ror":"https://ror.org/054d77k59","country_code":"PK","type":"education","lineage":["https://openalex.org/I61623833"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Tanveer","raw_affiliation_strings":["Department of Mathematics and Statistics, Sub-Campus Depalpur, University of Agriculture Faisalabad, Faisalabad 38000, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-3118-571X","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Sub-Campus Depalpur, University of Agriculture Faisalabad, Faisalabad 38000, Pakistan","institution_ids":["https://openalex.org/I4210147796","https://openalex.org/I61623833"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055573564","display_name":"Muhammad Usman","orcid":"https://orcid.org/0000-0003-1919-862X"},"institutions":[{"id":"https://openalex.org/I195024194","display_name":"Riphah International University","ror":"https://ror.org/02kdm5630","country_code":"PK","type":"education","lineage":["https://openalex.org/I195024194"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Usman","raw_affiliation_strings":["Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University, Lahore 54000, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University, Lahore 54000, Pakistan","institution_ids":["https://openalex.org/I195024194"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000749979","display_name":"D. K. Almutairi","orcid":"https://orcid.org/0000-0003-1275-2384"},"institutions":[{"id":"https://openalex.org/I195631090","display_name":"Majmaah University","ror":"https://ror.org/01mcrnj60","country_code":"SA","type":"education","lineage":["https://openalex.org/I195631090"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Dalal Almutairi","raw_affiliation_strings":["Department of Mathematics, College of Science, Al Zulfi Majmaah University, Al Majmaah 11952, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-1275-2384","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, Al Zulfi Majmaah University, Al Majmaah 11952, Saudi Arabia","institution_ids":["https://openalex.org/I195631090"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089070491","display_name":"Rabab Alharbi","orcid":"https://orcid.org/0000-0003-4994-833X"},"institutions":[{"id":"https://openalex.org/I156216236","display_name":"Qassim University","ror":"https://ror.org/01wsfe280","country_code":"SA","type":"education","lineage":["https://openalex.org/I156216236"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Rabab Alharbi","raw_affiliation_strings":["Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-4994-833X","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia","institution_ids":["https://openalex.org/I156216236"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":5.5581,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.94874423,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":98},"biblio":{"volume":"14","issue":"2","first_page":"118","last_page":"118"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9373999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9373999834060669,"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/riccati-equation","display_name":"Riccati equation","score":0.703149676322937},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6061305999755859},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5646933317184448},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5612056255340576},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5158185362815857},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5089163780212402},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.5050919651985168},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.44311487674713135},{"id":"https://openalex.org/keywords/exponential-type","display_name":"Exponential type","score":0.4153728485107422},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2804381847381592},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.22119098901748657},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2023869752883911},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11864981055259705},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.10918974876403809},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.05116957426071167},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.04820293188095093}],"concepts":[{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.703149676322937},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6061305999755859},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5646933317184448},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5612056255340576},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5158185362815857},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5089163780212402},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.5050919651985168},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.44311487674713135},{"id":"https://openalex.org/C103642545","wikidata":"https://www.wikidata.org/wiki/Q5421531","display_name":"Exponential type","level":2,"score":0.4153728485107422},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2804381847381592},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.22119098901748657},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2023869752883911},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11864981055259705},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.10918974876403809},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.05116957426071167},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.04820293188095093},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms14020118","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14020118","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:e093ecfdcafd49ae84d065427979936f","is_oa":false,"landing_page_url":"https://doaj.org/article/e093ecfdcafd49ae84d065427979936f","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":"Axioms, Vol 14, Iss 2, p 118 (2025)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/14/2/118/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms14020118","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Pages: 118","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms14020118","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14020118","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W565587792","https://openalex.org/W1608917902","https://openalex.org/W1991566479","https://openalex.org/W1995123739","https://openalex.org/W2008670106","https://openalex.org/W2014313162","https://openalex.org/W2026269993","https://openalex.org/W2031597801","https://openalex.org/W2032800569","https://openalex.org/W2054243086","https://openalex.org/W2077145056","https://openalex.org/W2092091527","https://openalex.org/W2132101421","https://openalex.org/W2155969518","https://openalex.org/W2295026352","https://openalex.org/W2729797951","https://openalex.org/W2794740122","https://openalex.org/W2915871963","https://openalex.org/W2937463852","https://openalex.org/W3043916206","https://openalex.org/W3047204195","https://openalex.org/W4226190337","https://openalex.org/W4247571700","https://openalex.org/W4313580927","https://openalex.org/W4387057526","https://openalex.org/W6634636746","https://openalex.org/W6719499431","https://openalex.org/W6737228366","https://openalex.org/W6738023688"],"related_works":["https://openalex.org/W4297426666","https://openalex.org/W2952204569","https://openalex.org/W2794088623","https://openalex.org/W2046360005","https://openalex.org/W2530543162","https://openalex.org/W3042136779","https://openalex.org/W3025504071","https://openalex.org/W3036249437","https://openalex.org/W1633561714","https://openalex.org/W4327779305"],"abstract_inverted_index":{"Fuzzy":[0],"systems":[1],"play":[2],"a":[3,35,48],"crucial":[4],"role":[5],"in":[6,22],"emerging":[7],"fields":[8],"such":[9],"as":[10,59,61],"artificial":[11],"intelligence,":[12],"machine":[13],"learning,":[14],"and":[15,64,82],"computer":[16],"science,":[17],"drawing":[18],"significant":[19],"research":[20],"interest":[21],"fuzzy":[23,39,52],"difference":[24,40,53],"equations.":[25,54],"Inspired":[26],"by":[27],"this,":[28],"we":[29],"analyze":[30],"the":[31,57,62,72],"dynamic":[32],"properties":[33],"of":[34,50,67],"fourth-order":[36,51],"exponential":[37],"Riccati-type":[38],"equation.":[41],"The":[42],"study":[43],"is":[44],"further":[45],"extended":[46],"to":[47],"system":[49],"We":[55],"investigate":[56],"boundedness,":[58],"well":[60],"local":[63],"global":[65],"stability,":[66],"positive":[68],"solutions.":[69],"To":[70],"support":[71],"theoretical":[73],"findings,":[74],"numerical":[75],"examples":[76],"are":[77],"presented":[78],"along":[79],"with":[80],"graphical":[81],"tabular":[83],"representations.":[84]},"counts_by_year":[{"year":2025,"cited_by_count":4}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}