{"id":"https://openalex.org/W4389980099","doi":"https://doi.org/10.1051/ro/2023194","title":"Stability analysis of fuzzy differential equation for prey\u2013predator system under<i>Z</i>-number fuzzy and granular differentiability concept","display_name":"Stability analysis of fuzzy differential equation for prey\u2013predator system under<i>Z</i>-number fuzzy and granular differentiability concept","publication_year":2023,"publication_date":"2023-12-19","ids":{"openalex":"https://openalex.org/W4389980099","doi":"https://doi.org/10.1051/ro/2023194"},"language":"en","primary_location":{"id":"doi:10.1051/ro/2023194","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ro/2023194","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2024/01/ro230447.pdf","source":{"id":"https://openalex.org/S4393919633","display_name":"RAIRO. Operations research","issn_l":"2804-7303","issn":["2804-7303"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.rairo-ro.org/articles/ro/pdf/2024/01/ro230447.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015677670","display_name":"S. Hati","orcid":null},"institutions":[{"id":"https://openalex.org/I155837530","display_name":"National Institute of Technology Durgapur","ror":"https://ror.org/04ds0jm32","country_code":"IN","type":"education","lineage":["https://openalex.org/I155837530"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Santu Hati","raw_affiliation_strings":["Department of Mathematics, National Institute of Technology Durgapur, Durgapur 721309, West Bengal, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Institute of Technology Durgapur, Durgapur 721309, West Bengal, India","institution_ids":["https://openalex.org/I155837530"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042305515","display_name":"Goutam Panigrahi","orcid":"https://orcid.org/0000-0002-4919-8439"},"institutions":[{"id":"https://openalex.org/I155837530","display_name":"National Institute of Technology Durgapur","ror":"https://ror.org/04ds0jm32","country_code":"IN","type":"education","lineage":["https://openalex.org/I155837530"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Goutam Panigrahi","raw_affiliation_strings":["Department of Mathematics, National Institute of Technology Durgapur, Durgapur 721309, West Bengal, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Institute of Technology Durgapur, Durgapur 721309, West Bengal, India","institution_ids":["https://openalex.org/I155837530"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063380569","display_name":"K. Maity","orcid":"https://orcid.org/0000-0001-6961-4148"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kalipada Maity","raw_affiliation_strings":["Department of Mathematics, Mugberia Gangadhar Mahavidyalaya, Bhupatinagar, Purba Medinipur 721425, West Bengal, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Mugberia Gangadhar Mahavidyalaya, Bhupatinagar, Purba Medinipur 721425, West Bengal, India","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5015677670"],"corresponding_institution_ids":["https://openalex.org/I155837530"],"apc_list":null,"apc_paid":null,"fwci":1.0042,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.79313211,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"58","issue":"1","first_page":"759","last_page":"774"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9882000088691711,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"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":0.988099992275238,"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/mathematics","display_name":"Mathematics","score":0.6352177858352661},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.6185300350189209},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.52668297290802},{"id":"https://openalex.org/keywords/predation","display_name":"Predation","score":0.519242525100708},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5103258490562439},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.5084144473075867},{"id":"https://openalex.org/keywords/predator","display_name":"Predator","score":0.42371976375579834},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.41885942220687866},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3801282048225403},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.323943167924881},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18665006756782532},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.12895235419273376},{"id":"https://openalex.org/keywords/ecology","display_name":"Ecology","score":0.10424119234085083},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09513762593269348},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.0843818187713623}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6352177858352661},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6185300350189209},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.52668297290802},{"id":"https://openalex.org/C188382862","wikidata":"https://www.wikidata.org/wiki/Q170430","display_name":"Predation","level":2,"score":0.519242525100708},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5103258490562439},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.5084144473075867},{"id":"https://openalex.org/C96857902","wikidata":"https://www.wikidata.org/wiki/Q2138108","display_name":"Predator","level":3,"score":0.42371976375579834},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.41885942220687866},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3801282048225403},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.323943167924881},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18665006756782532},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.12895235419273376},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.10424119234085083},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09513762593269348},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0843818187713623},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1051/ro/2023194","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ro/2023194","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2024/01/ro230447.pdf","source":{"id":"https://openalex.org/S4393919633","display_name":"RAIRO. Operations research","issn_l":"2804-7303","issn":["2804-7303"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1051/ro/2023194","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ro/2023194","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2024/01/ro230447.pdf","source":{"id":"https://openalex.org/S4393919633","display_name":"RAIRO. Operations research","issn_l":"2804-7303","issn":["2804-7303"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3737256009","display_name":null,"funder_award_id":"[475(Sanc.)/ST/P/S&T/16G-31/2018 dated 15.03.2019","funder_id":"https://openalex.org/F4320325376","funder_display_name":"Department of Science and Technology, Government of West Bengal"},{"id":"https://openalex.org/G4109052903","display_name":null,"funder_award_id":"dated","funder_id":"https://openalex.org/F4320320717","funder_display_name":"Department of Biotechnology, Ministry of Science and Technology, India"},{"id":"https://openalex.org/G8818784359","display_name":null,"funder_award_id":"HRD-11011/161/2020-HRD-DBT","funder_id":"https://openalex.org/F4320320717","funder_display_name":"Department of Biotechnology, Ministry of Science and Technology, India"}],"funders":[{"id":"https://openalex.org/F4320320717","display_name":"Department of Biotechnology, Ministry of Science and Technology, India","ror":"https://ror.org/03tjsyq23"},{"id":"https://openalex.org/F4320325376","display_name":"Department of Science and Technology, Government of West Bengal","ror":"https://ror.org/0101xrq71"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4389980099.pdf"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W1595992588","https://openalex.org/W1974378750","https://openalex.org/W1979776153","https://openalex.org/W1987899918","https://openalex.org/W1992777250","https://openalex.org/W2008403791","https://openalex.org/W2014496328","https://openalex.org/W2026469152","https://openalex.org/W2032731999","https://openalex.org/W2038354216","https://openalex.org/W2042774699","https://openalex.org/W2057805880","https://openalex.org/W2060761040","https://openalex.org/W2077035544","https://openalex.org/W2085139922","https://openalex.org/W2089021392","https://openalex.org/W2090600240","https://openalex.org/W2096768134","https://openalex.org/W2116027179","https://openalex.org/W2145213161","https://openalex.org/W2150175407","https://openalex.org/W2158380130","https://openalex.org/W2507537394","https://openalex.org/W2580890888","https://openalex.org/W2606552586","https://openalex.org/W2736430830","https://openalex.org/W2739633147","https://openalex.org/W2774810271","https://openalex.org/W2793584758","https://openalex.org/W2941877913","https://openalex.org/W3008061058","https://openalex.org/W3087973074","https://openalex.org/W3090479667","https://openalex.org/W3091978395","https://openalex.org/W3189196468","https://openalex.org/W4211007335","https://openalex.org/W4311827766","https://openalex.org/W4322774228","https://openalex.org/W4378363872"],"related_works":["https://openalex.org/W2168669462","https://openalex.org/W2067000585","https://openalex.org/W2192426841","https://openalex.org/W4323811225","https://openalex.org/W2164070575","https://openalex.org/W4311356582","https://openalex.org/W2289298756","https://openalex.org/W2073795128","https://openalex.org/W2143533297","https://openalex.org/W2075391697"],"abstract_inverted_index":{"The":[0,21,96],"stability":[1,24,100],"analysis":[2,25,105],"is":[3,33,48,85,101],"one":[4],"of":[5,12,23,38,76,98,108,123,131],"the":[6,10,36,39,46,73,77,106,129,132],"basic":[7],"problems":[8],"in":[9],"field":[11],"system,":[13],"prey\u2013predator,":[14],"production":[15,29,116],"inventory":[16,30,117],"control,":[17],"signal":[18],"processing":[19],"etc.":[20],"goal":[22],"for":[26],"prey\u2013predator":[27,57,74,83],"and":[28,42,62,134],"control":[31],"model":[32,58,84,91,118],"to":[34,87,127],"determine":[35],"region":[37],"different":[40],"variables":[41],"parameters":[43,75],"at":[44],"which":[45],"system":[47,78,126],"stable":[49],"or":[50],"unstable.":[51],"This":[52,81],"paper":[53],"explores":[54],"an":[55,88],"uncertain":[56],"where":[59],"both":[60],"prey":[61],"predator":[63],"populations":[64],"are":[65,79],"fuzzy":[66,82,124],"variables.":[67],"Also":[68],"we":[69,113],"have":[70],"considered":[71],"all":[72],"imprecise.":[80],"converted":[86],"equivalent":[89],"crisp":[90],"using":[92],"granular":[93],"differentiability":[94],"approach.":[95],"condition":[97],"local":[99],"obtained":[102],"mathematically":[103],"by":[104],"eigenvalues":[107],"characteristic":[109],"equation.":[110],"And":[111],"also":[112],"introduced":[114],"a":[115,120],"as":[119],"case":[121],"study":[122],"dynamical":[125],"illustrate":[128],"efficiency":[130],"result":[133],"practical":[135],"aspects.":[136]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}