{"id":"https://openalex.org/W7204276443","doi":"https://doi.org/10.30598/barekengvol20iss4pp3223-3240","title":"DYNAMICAL ANALYSIS OF TWO LOAN CATEGORIES IN A BANKING SYSTEM WITH NON-PERFORMING LOANS","display_name":"DYNAMICAL ANALYSIS OF TWO LOAN CATEGORIES IN A BANKING SYSTEM WITH NON-PERFORMING LOANS","publication_year":2026,"publication_date":"2026-08-24","ids":{"openalex":"https://openalex.org/W7204276443","doi":"https://doi.org/10.30598/barekengvol20iss4pp3223-3240"},"language":"en","primary_location":{"id":"doi:10.30598/barekengvol20iss4pp3223-3240","doi":"https://doi.org/10.30598/barekengvol20iss4pp3223-3240","is_oa":true,"landing_page_url":"https://doi.org/10.30598/barekengvol20iss4pp3223-3240","pdf_url":"https://ojs3.unpatti.ac.id/index.php/barekeng/article/download/22267/13189","source":{"id":"https://openalex.org/S4210230638","display_name":"BAREKENG JURNAL ILMU MATEMATIKA DAN TERAPAN","issn_l":"1978-7227","issn":["1978-7227","2615-3017"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj","jufo-1"],"host_organization":"https://openalex.org/P4310314943","host_organization_name":"University of Pattimura","host_organization_lineage":["https://openalex.org/P4310314943"],"host_organization_lineage_names":["University of Pattimura"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"BAREKENG: Jurnal Ilmu Matematika dan Terapan","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://ojs3.unpatti.ac.id/index.php/barekeng/article/download/22267/13189","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5116100746","display_name":"Onik Febria Damayanti","orcid":"https://orcid.org/0009-0008-4530-8224","observed_orcids":["https://orcid.org/0009-0008-4530-8224"]},"institutions":[{"id":"https://openalex.org/I177055848","display_name":"University of Brawijaya","ror":"https://ror.org/01wk3d929","country_code":"ID","type":"education","lineage":["https://openalex.org/I177055848"]}],"countries":["ID"],"is_corresponding":false,"raw_author_name":"Onik Febria Damayanti","raw_affiliation_strings":["Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Brawijaya, Indonesia"],"raw_orcid":"https://orcid.org/0009-0008-4530-8224","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Brawijaya, Indonesia","institution_ids":["https://openalex.org/I177055848"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039090534","display_name":"\u0130snani Darti","orcid":"https://orcid.org/0000-0002-4163-8030","observed_orcids":["https://orcid.org/0000-0002-4163-8030"]},"institutions":[{"id":"https://openalex.org/I177055848","display_name":"University of Brawijaya","ror":"https://ror.org/01wk3d929","country_code":"ID","type":"education","lineage":["https://openalex.org/I177055848"]}],"countries":["ID"],"is_corresponding":false,"raw_author_name":"Isnani Darti","raw_affiliation_strings":["Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Brawijaya, Indonesia"],"raw_orcid":"https://orcid.org/0000-0002-4163-8030","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Brawijaya, Indonesia","institution_ids":["https://openalex.org/I177055848"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010441443","display_name":"Agus Suryanto","orcid":"https://orcid.org/0000-0002-1335-5631","observed_orcids":["https://orcid.org/0000-0002-1335-5631"]},"institutions":[{"id":"https://openalex.org/I177055848","display_name":"University of Brawijaya","ror":"https://ror.org/01wk3d929","country_code":"ID","type":"education","lineage":["https://openalex.org/I177055848"]}],"countries":["ID"],"is_corresponding":false,"raw_author_name":"Agus Suryanto","raw_affiliation_strings":["Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Brawijaya, Indonesia"],"raw_orcid":"https://orcid.org/0000-0002-1335-5631","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Brawijaya, Indonesia","institution_ids":["https://openalex.org/I177055848"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026880072","display_name":"Nur Shofianah","orcid":"https://orcid.org/0000-0002-6708-8698","observed_orcids":["https://orcid.org/0000-0002-6708-8698"]},"institutions":[{"id":"https://openalex.org/I177055848","display_name":"University of Brawijaya","ror":"https://ror.org/01wk3d929","country_code":"ID","type":"education","lineage":["https://openalex.org/I177055848"]}],"countries":["ID"],"is_corresponding":false,"raw_author_name":"Nur Shofianah","raw_affiliation_strings":["Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Brawijaya, Indonesia"],"raw_orcid":"https://orcid.org/0000-0002-6708-8698","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Brawijaya, Indonesia","institution_ids":["https://openalex.org/I177055848"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056004498","display_name":"Trisilowati Trisilowati","orcid":"https://orcid.org/0000-0001-5989-1133","observed_orcids":["https://orcid.org/0000-0001-5989-1133"]},"institutions":[{"id":"https://openalex.org/I177055848","display_name":"University of Brawijaya","ror":"https://ror.org/01wk3d929","country_code":"ID","type":"education","lineage":["https://openalex.org/I177055848"]}],"countries":["ID"],"is_corresponding":false,"raw_author_name":"Trisilowati Trisilowati","raw_affiliation_strings":["Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Brawijaya, Indonesia"],"raw_orcid":"https://orcid.org/0000-0001-5989-1133","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Brawijaya, Indonesia","institution_ids":["https://openalex.org/I177055848"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I177055848"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"20","issue":"4","first_page":"3223","last_page":"3240"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10127","display_name":"Banking stability, regulation, efficiency","score":0.9765999913215637,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10127","display_name":"Banking stability, regulation, efficiency","score":0.9765999913215637,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.010599999688565731,"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/T14183","display_name":"Banking Sector Performance and Management","score":0.0032999999821186066,"subfield":{"id":"https://openalex.org/subfields/1402","display_name":"Accounting"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/non-performing-loans","display_name":"non-performing loans","score":0.9980000257492065},{"id":"https://openalex.org/keywords/bank-stability","display_name":"bank stability","score":0.8550000190734863},{"id":"https://openalex.org/keywords/predator-prey-model","display_name":"predator-prey model","score":0.8930000066757202},{"id":"https://openalex.org/keywords/bank-deposits","display_name":"bank deposits","score":0.5920000076293945},{"id":"https://openalex.org/keywords/individual-loans","display_name":"individual loans","score":0.8399999737739563},{"id":"https://openalex.org/keywords/corporate-lending","display_name":"corporate lending","score":0.8109999895095825},{"id":"https://openalex.org/keywords/stability-of-equilibrium","display_name":"equilibrium stability","score":0.5889999866485596},{"id":"https://openalex.org/keywords/global-asymptotic-stability","display_name":"global asymptotic stability","score":0.9190000295639038},{"id":"https://openalex.org/keywords/credit-intermediation","display_name":"credit intermediation","score":0.7919999957084656},{"id":"https://openalex.org/keywords/nonlinear-dynamical-systems","display_name":"nonlinear dynamical systems","score":0.6859999895095825}],"concepts":[{"id":"https://openalex.org/C2777764128","wikidata":"https://www.wikidata.org/wiki/Q189539","display_name":"Loan","level":2,"score":0.7854999899864197},{"id":"https://openalex.org/C71387314","wikidata":"https://www.wikidata.org/wiki/Q494128","display_name":"Non-performing loan","level":3,"score":0.5863999724388123},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5608000159263611},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.5056999921798706},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.4684999883174896},{"id":"https://openalex.org/C65146658","wikidata":"https://www.wikidata.org/wiki/Q1416431","display_name":"Financial intermediary","level":2,"score":0.46560001373291016},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.45739999413490295},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4505999982357025},{"id":"https://openalex.org/C2779143981","wikidata":"https://www.wikidata.org/wiki/Q1445414","display_name":"Intermediation","level":2,"score":0.4478999972343445},{"id":"https://openalex.org/C556758197","wikidata":"https://www.wikidata.org/wiki/Q580018","display_name":"Monetary economics","level":1,"score":0.44449999928474426},{"id":"https://openalex.org/C41949839","wikidata":"https://www.wikidata.org/wiki/Q1756677","display_name":"Stability theory","level":3,"score":0.3865000009536743},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.3765000104904175},{"id":"https://openalex.org/C103382277","wikidata":"https://www.wikidata.org/wiki/Q282640","display_name":"General equilibrium theory","level":2,"score":0.3458999991416931},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.3292999863624573},{"id":"https://openalex.org/C73283319","wikidata":"https://www.wikidata.org/wiki/Q1416617","display_name":"Financial system","level":1,"score":0.32429999113082886},{"id":"https://openalex.org/C162118730","wikidata":"https://www.wikidata.org/wiki/Q1128453","display_name":"Actuarial science","level":1,"score":0.3199000060558319},{"id":"https://openalex.org/C175025494","wikidata":"https://www.wikidata.org/wiki/Q179179","display_name":"Interest rate","level":2,"score":0.31869998574256897},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.2989000082015991},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2897999882698059},{"id":"https://openalex.org/C2992337254","wikidata":"https://www.wikidata.org/wiki/Q31275820","display_name":"Financial stability","level":2,"score":0.28700000047683716},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27810001373291016},{"id":"https://openalex.org/C139569457","wikidata":"https://www.wikidata.org/wiki/Q1666223","display_name":"Intermediary","level":2,"score":0.27810001373291016},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.2777999937534332},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2678999900817871},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.26739999651908875},{"id":"https://openalex.org/C178350159","wikidata":"https://www.wikidata.org/wiki/Q162714","display_name":"Credit risk","level":2,"score":0.25929999351501465},{"id":"https://openalex.org/C120527767","wikidata":"https://www.wikidata.org/wiki/Q3196867","display_name":"Debt","level":2,"score":0.2572000026702881},{"id":"https://openalex.org/C175444787","wikidata":"https://www.wikidata.org/wiki/Q39072","display_name":"Microeconomics","level":1,"score":0.25029999017715454}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.30598/barekengvol20iss4pp3223-3240","doi":"https://doi.org/10.30598/barekengvol20iss4pp3223-3240","is_oa":true,"landing_page_url":"https://doi.org/10.30598/barekengvol20iss4pp3223-3240","pdf_url":"https://ojs3.unpatti.ac.id/index.php/barekeng/article/download/22267/13189","source":{"id":"https://openalex.org/S4210230638","display_name":"BAREKENG JURNAL ILMU MATEMATIKA DAN TERAPAN","issn_l":"1978-7227","issn":["1978-7227","2615-3017"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj","jufo-1"],"host_organization":"https://openalex.org/P4310314943","host_organization_name":"University of Pattimura","host_organization_lineage":["https://openalex.org/P4310314943"],"host_organization_lineage_names":["University of Pattimura"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"BAREKENG: Jurnal Ilmu Matematika dan Terapan","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:212afd9129b141b2ae24bd8e52e34a45","doi":null,"is_oa":false,"landing_page_url":"https://doaj.org/article/212afd9129b141b2ae24bd8e52e34a45","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,"listed_in":[],"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":"Barekeng, Vol 20, Iss 4 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.30598/barekengvol20iss4pp3223-3240","doi":"https://doi.org/10.30598/barekengvol20iss4pp3223-3240","is_oa":true,"landing_page_url":"https://doi.org/10.30598/barekengvol20iss4pp3223-3240","pdf_url":"https://ojs3.unpatti.ac.id/index.php/barekeng/article/download/22267/13189","source":{"id":"https://openalex.org/S4210230638","display_name":"BAREKENG JURNAL ILMU MATEMATIKA DAN TERAPAN","issn_l":"1978-7227","issn":["1978-7227","2615-3017"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj","jufo-1"],"host_organization":"https://openalex.org/P4310314943","host_organization_name":"University of Pattimura","host_organization_lineage":["https://openalex.org/P4310314943"],"host_organization_lineage_names":["University of Pattimura"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"BAREKENG: Jurnal Ilmu Matematika dan Terapan","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1893314651","display_name":null,"funder_award_id":"02/UN10","funder_id":"https://openalex.org/F4320323817","funder_display_name":"Universitas Brawijaya"}],"funders":[{"id":"https://openalex.org/F4320323817","display_name":"Universitas Brawijaya","ror":"https://ror.org/01wk3d929"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204276443.pdf","grobid_xml":"https://content.openalex.org/works/W7204276443.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W176572674","https://openalex.org/W1968748439","https://openalex.org/W1989367774","https://openalex.org/W2080042604","https://openalex.org/W2332896151","https://openalex.org/W2410938517","https://openalex.org/W2786038494","https://openalex.org/W2982166002","https://openalex.org/W3005898125","https://openalex.org/W3081119821","https://openalex.org/W3095620776","https://openalex.org/W3152806430","https://openalex.org/W3169243604","https://openalex.org/W3193329388","https://openalex.org/W3193979577","https://openalex.org/W4206550036","https://openalex.org/W4242490430","https://openalex.org/W4388879265","https://openalex.org/W4390668062","https://openalex.org/W4396497827","https://openalex.org/W4402177045","https://openalex.org/W4407024454"],"related_works":["https://openalex.org/W4407024454","https://openalex.org/W1989367774","https://openalex.org/W4213185512","https://openalex.org/W7222607032","https://openalex.org/W7206154698","https://openalex.org/W2080042604","https://openalex.org/W3122750779","https://openalex.org/W7162125532","https://openalex.org/W4409176193","https://openalex.org/W3049218682"],"abstract_inverted_index":{"The":[0,24,79,97,108,143],"ability":[1],"of":[2,20,51,65,84,114,157,186,193],"banks":[3],"to":[4,11,111,136,152,170],"extend":[5],"credit":[6],"and":[7,47,62,69,93,116,140,159,172,188],"meet":[8],"their":[9],"obligations":[10],"depositors":[12],"can":[13,34],"be":[14,35],"significantly":[15],"affected":[16],"by":[17],"the":[18,60,82,102,112,121,154,162,174,182,191],"presence":[19],"non-performing":[21],"loans":[22,68,117],"(NPL).":[23],"intermediation":[25],"process,":[26],"in":[27,195],"which":[28],"deposits":[29,58,115,187],"are":[30,125,168],"transformed":[31],"into":[32,181],"loans,":[33,66,71,189],"represented":[36],"through":[37],"a":[38,49,75],"predator\u2013prey":[39],"modeling":[40],"framework.":[41],"In":[42],"this":[43],"study,":[44],"we":[45],"formulate":[46],"analyze":[48],"system":[50,95,103,198],"three":[52],"nonlinear":[53],"ordinary":[54],"differential":[55],"equations":[56],"representing":[57],"as":[59,72,86],"prey":[61],"two":[63],"categories":[64],"individual":[67],"company":[70],"predators":[73],"within":[74],"single":[76],"banking":[77,163,197],"system.":[78,164],"model":[80],"incorporates":[81],"effect":[83],"NPLs":[85,194],"factors":[87],"that":[88,101,147],"reduce":[89,153],"effective":[90],"loan":[91,137],"performance":[92],"influence":[94],"interactions.":[96],"analytical":[98,175],"results":[99,178],"show":[100],"possesses":[104],"five":[105],"equilibrium":[106,109],"points.":[107],"corresponding":[110],"absence":[113],"is":[118],"unstable,":[119],"while":[120],"remaining":[122],"four":[123],"equilibria":[124,158],"globally":[126],"asymptotically":[127],"stable":[128],"under":[129],"specific":[130],"parameter":[131],"conditions,":[132],"particularly":[133],"those":[134],"related":[135],"growth":[138],"rates":[139,150],"NPL":[141,149],"levels.":[142],"stability":[144,155],"analysis":[145],"indicates":[146],"higher":[148],"tend":[151],"region":[156],"may":[160],"destabilize":[161],"Furthermore,":[165],"numerical":[166],"simulations":[167],"conducted":[169],"support":[171],"illustrate":[173],"findings.":[176],"These":[177],"provide":[179],"insight":[180],"long-term":[183],"dynamic":[184],"behavior":[185],"emphasizing":[190],"role":[192],"determining":[196],"stability.":[199]},"counts_by_year":[],"updated_date":"2026-11-13T13:42:25.865203","created_date":"2026-08-27T00:00:00"}