{"id":"https://openalex.org/W7203837280","doi":"https://doi.org/10.7906/indecs.24.6.6","title":"Mathematical Formalisation of Emergent Behaviour in Digital Twins of Manufacturing Systems","display_name":"Mathematical Formalisation of Emergent Behaviour in Digital Twins of Manufacturing Systems","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7203837280","doi":"https://doi.org/10.7906/indecs.24.6.6"},"language":"en","primary_location":{"id":"doi:10.7906/indecs.24.6.6","doi":"https://doi.org/10.7906/indecs.24.6.6","is_oa":true,"landing_page_url":"https://doi.org/10.7906/indecs.24.6.6","pdf_url":"https://www.indecs.eu/2026/indecs2026-pp752-760.pdf","source":{"id":"https://openalex.org/S58389884","display_name":"Interdisciplinary Description of Complex Systems","issn_l":"1334-4676","issn":["1334-4676","1334-4684","1334-5230"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","ddh","doaj","erih-plus","norway-1","poland-40","russia-white-list-3","vabb-shw"],"host_organization":"https://openalex.org/P4310314824","host_organization_name":"Croatian Interdisciplinary Society","host_organization_lineage":["https://openalex.org/P4310314824"],"host_organization_lineage_names":["Croatian Interdisciplinary Society"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Interdisciplinary Description of Complex Systems","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://www.indecs.eu/2026/indecs2026-pp752-760.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043366937","display_name":"Sergiy Kovalevskyy","orcid":"https://orcid.org/0000-0002-4708-4091","observed_orcids":["https://orcid.org/0000-0002-4708-4091"]},"institutions":[{"id":"https://openalex.org/I4210121817","display_name":"Donbass State Engineering Academy","ror":"https://ror.org/02k14cb26","country_code":"UA","type":"education","lineage":["https://openalex.org/I4210121817"]}],"countries":["UA"],"is_corresponding":true,"raw_author_name":"Sergiy Kovalevskyy","raw_affiliation_strings":["Donbas State Engineering Academy , Kramatorsk-Khust , Ukraine","Donbas State Engineering Academy Kram\u0430torsk-Khust , Ukraine"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Donbas State Engineering Academy , Kramatorsk-Khust , Ukraine","institution_ids":["https://openalex.org/I4210121817"]},{"raw_affiliation_string":"Donbas State Engineering Academy Kram\u0430torsk-Khust , Ukraine","institution_ids":["https://openalex.org/I4210121817"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5043366937"],"corresponding_institution_ids":["https://openalex.org/I4210121817"],"apc_list":null,"apc_paid":null,"fwci":2.1296,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.80802257,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"24","issue":"6","first_page":"752","last_page":"760"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10763","display_name":"Digital Transformation in Industry","score":0.48750001192092896,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10763","display_name":"Digital Transformation in Industry","score":0.48750001192092896,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T14299","display_name":"Complex Systems and Dynamics","score":0.45730000734329224,"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/T12000","display_name":"Systems Engineering Methodologies and Applications","score":0.007699999958276749,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/digital-twin","display_name":"digital twin","score":0.9610000252723694},{"id":"https://openalex.org/keywords/emergent-behavior","display_name":"emergent behavior","score":0.9580000042915344},{"id":"https://openalex.org/keywords/manufacturing-systems","display_name":"manufacturing systems","score":0.9480000138282776},{"id":"https://openalex.org/keywords/complex-systems","display_name":"complex systems","score":0.7599999904632568},{"id":"https://openalex.org/keywords/subsystem-interaction","display_name":"subsystem interaction","score":0.7979999780654907},{"id":"https://openalex.org/keywords/differential-equation-model","display_name":"differential equation model","score":0.5220000147819519},{"id":"https://openalex.org/keywords/stability-theorems","display_name":"stability theorems","score":0.949999988079071},{"id":"https://openalex.org/keywords/variational-principle","display_name":"variational principle","score":0.9020000100135803},{"id":"https://openalex.org/keywords/information-theoretic-complexity","display_name":"information-theoretic complexity","score":0.8410000205039978},{"id":"https://openalex.org/keywords/manufacturing-efficiency","display_name":"manufacturing efficiency","score":0.8870000243186951},{"id":"https://openalex.org/keywords/industry-5-0","display_name":"Industry 5.0","score":0.9440000057220459},{"id":"https://openalex.org/keywords/intelligent-control","display_name":"intelligent control","score":0.9089999794960022}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5052000284194946},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.3946000039577484},{"id":"https://openalex.org/C201995342","wikidata":"https://www.wikidata.org/wiki/Q682496","display_name":"Systems engineering","level":1,"score":0.36579999327659607},{"id":"https://openalex.org/C13736549","wikidata":"https://www.wikidata.org/wiki/Q4489420","display_name":"Industrial engineering","level":1,"score":0.3393000066280365},{"id":"https://openalex.org/C58328972","wikidata":"https://www.wikidata.org/wiki/Q184609","display_name":"Expert system","level":2,"score":0.3230000138282776},{"id":"https://openalex.org/C117671659","wikidata":"https://www.wikidata.org/wiki/Q11049265","display_name":"Manufacturing engineering","level":1,"score":0.30649998784065247},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.29649999737739563},{"id":"https://openalex.org/C539667460","wikidata":"https://www.wikidata.org/wiki/Q2414942","display_name":"Management science","level":1,"score":0.2808000147342682},{"id":"https://openalex.org/C76969082","wikidata":"https://www.wikidata.org/wiki/Q486902","display_name":"Mathematical model","level":2,"score":0.26750001311302185},{"id":"https://openalex.org/C53688548","wikidata":"https://www.wikidata.org/wiki/Q1122190","display_name":"Computer-integrated manufacturing","level":2,"score":0.26600000262260437},{"id":"https://openalex.org/C2780841897","wikidata":"https://www.wikidata.org/wiki/Q25349015","display_name":"Digital manufacturing","level":2,"score":0.257999986410141}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.7906/indecs.24.6.6","doi":"https://doi.org/10.7906/indecs.24.6.6","is_oa":true,"landing_page_url":"https://doi.org/10.7906/indecs.24.6.6","pdf_url":"https://www.indecs.eu/2026/indecs2026-pp752-760.pdf","source":{"id":"https://openalex.org/S58389884","display_name":"Interdisciplinary Description of Complex Systems","issn_l":"1334-4676","issn":["1334-4676","1334-4684","1334-5230"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","ddh","doaj","erih-plus","norway-1","poland-40","russia-white-list-3","vabb-shw"],"host_organization":"https://openalex.org/P4310314824","host_organization_name":"Croatian Interdisciplinary Society","host_organization_lineage":["https://openalex.org/P4310314824"],"host_organization_lineage_names":["Croatian Interdisciplinary Society"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Interdisciplinary Description of Complex Systems","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.7906/indecs.24.6.6","doi":"https://doi.org/10.7906/indecs.24.6.6","is_oa":true,"landing_page_url":"https://doi.org/10.7906/indecs.24.6.6","pdf_url":"https://www.indecs.eu/2026/indecs2026-pp752-760.pdf","source":{"id":"https://openalex.org/S58389884","display_name":"Interdisciplinary Description of Complex Systems","issn_l":"1334-4676","issn":["1334-4676","1334-4684","1334-5230"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","ddh","doaj","erih-plus","norway-1","poland-40","russia-white-list-3","vabb-shw"],"host_organization":"https://openalex.org/P4310314824","host_organization_name":"Croatian Interdisciplinary Society","host_organization_lineage":["https://openalex.org/P4310314824"],"host_organization_lineage_names":["Croatian Interdisciplinary Society"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Interdisciplinary Description of Complex Systems","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/9","score":0.5378999710083008,"display_name":"Industry, innovation and infrastructure"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7203837280.pdf","grobid_xml":"https://content.openalex.org/works/W7203837280.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W1544145404","https://openalex.org/W1995875735","https://openalex.org/W2518003110","https://openalex.org/W2757110387","https://openalex.org/W2890904471","https://openalex.org/W2976301483","https://openalex.org/W3003667836","https://openalex.org/W3042091195"],"related_works":["https://openalex.org/W7162128364","https://openalex.org/W3213707165","https://openalex.org/W4386880950","https://openalex.org/W4318820900","https://openalex.org/W4318820818","https://openalex.org/W4391382111","https://openalex.org/W7168097362","https://openalex.org/W3216943813","https://openalex.org/W2954744366","https://openalex.org/W3185810042"],"abstract_inverted_index":{"The":[0],"rapid":[1],"development":[2],"of":[3,15,42,55,71,82,89,112],"digital":[4,23,69,74],"twin":[5,75],"technology":[6],"has":[7],"created":[8],"new":[9],"opportunities":[10],"for":[11,64,139],"modelling":[12],"and":[13,29,103],"optimisation":[14],"complex":[16,43],"manufacturing":[17,72,123],"systems.However,":[18],"most":[19],"existing":[20],"studies":[21],"treat":[22],"twins":[24,70],"primarily":[25],"as":[26,78],"simulation":[27],"tools":[28],"seldom":[30],"address":[31],"emergent":[32,66],"behaviour":[33,48,67],"arising":[34],"from":[35],"subsystem":[36],"interactions.Emergence":[37],"is":[38,76,95,116],"a":[39,61,79,87,137],"fundamental":[40],"property":[41],"systems":[44],"in":[45,68,142],"which":[46],"global":[47],"cannot":[49],"be":[50],"reduced":[51],"to":[52,97,122],"the":[53,131],"sum":[54],"individual":[56],"component":[57],"behaviours.This":[58],"article":[59],"proposes":[60],"mathematical":[62],"framework":[63],"analysing":[65],"systems.The":[73],"modelled":[77],"dynamic":[80],"network":[81],"interacting":[83],"subsystems":[84],"described":[85],"by":[86],"system":[88],"differential":[90],"equations.An":[91],"entropy-based":[92],"emergence":[93],"index":[94],"introduced":[96],"quantify":[98],"collective":[99],"complexity.Two":[100],"stability":[101],"theorems":[102],"one":[104],"optimality":[105],"theorem":[106],"are":[107],"formally":[108],"proved.A":[109],"variational":[110],"Principle":[111],"Minimum":[113],"Emergent":[114],"Complexity":[115],"formulated,":[117],"linking":[118],"information-theoretic":[119],"complexity":[120],"directly":[121],"efficiency.Numerical":[124],"simulations":[125],"with":[126],"four":[127],"scientific":[128],"figures":[129],"confirm":[130],"theoretical":[132],"predictions.The":[133],"proposed":[134],"formalisation":[135],"provides":[136],"foundation":[138],"intelligent":[140],"control":[141],"Industry":[143],"5.0":[144],"environments.":[145]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2026-08-21T00:00:00"}