{"id":"https://openalex.org/W3120551547","doi":"https://doi.org/10.3390/e23010103","title":"A Novel Measure Inspired by Lyapunov Exponents for the Characterization of Dynamics in State-Transition Networks","display_name":"A Novel Measure Inspired by Lyapunov Exponents for the Characterization of Dynamics in State-Transition Networks","publication_year":2021,"publication_date":"2021-01-12","ids":{"openalex":"https://openalex.org/W3120551547","doi":"https://doi.org/10.3390/e23010103","mag":"3120551547","pmid":"https://pubmed.ncbi.nlm.nih.gov/33445685"},"language":"en","primary_location":{"id":"doi:10.3390/e23010103","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23010103","pdf_url":"https://www.mdpi.com/1099-4300/23/1/103/pdf?version=1611303693","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/23/1/103/pdf?version=1611303693","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023524348","display_name":"Bulcs\u00fa S\u00e1ndor","orcid":"https://orcid.org/0000-0003-4887-7859"},"institutions":[{"id":"https://openalex.org/I3125347698","display_name":"Babe\u0219-Bolyai University","ror":"https://ror.org/02rmd1t30","country_code":"RO","type":"education","lineage":["https://openalex.org/I3125347698"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"Bulcs\u00fa S\u00e1ndor","raw_affiliation_strings":["Department of Physics, Babes-Bolyai University, 400084 Cluj-Napoca, Romania"],"raw_orcid":"https://orcid.org/0000-0003-4887-7859","affiliations":[{"raw_affiliation_string":"Department of Physics, Babes-Bolyai University, 400084 Cluj-Napoca, Romania","institution_ids":["https://openalex.org/I3125347698"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007448068","display_name":"Bence Schneider","orcid":"https://orcid.org/0000-0002-6910-7258"},"institutions":[{"id":"https://openalex.org/I3125347698","display_name":"Babe\u0219-Bolyai University","ror":"https://ror.org/02rmd1t30","country_code":"RO","type":"education","lineage":["https://openalex.org/I3125347698"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Bence Schneider","raw_affiliation_strings":["Department of Physics, Babes-Bolyai University, 400084 Cluj-Napoca, Romania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, Babes-Bolyai University, 400084 Cluj-Napoca, Romania","institution_ids":["https://openalex.org/I3125347698"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002638169","display_name":"Zsolt I. L\u00e1z\u00e1r","orcid":"https://orcid.org/0000-0001-7356-1683"},"institutions":[{"id":"https://openalex.org/I3125347698","display_name":"Babe\u0219-Bolyai University","ror":"https://ror.org/02rmd1t30","country_code":"RO","type":"education","lineage":["https://openalex.org/I3125347698"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Zsolt I. L\u00e1z\u00e1r","raw_affiliation_strings":["Department of Physics, Babes-Bolyai University, 400084 Cluj-Napoca, Romania"],"raw_orcid":"https://orcid.org/0000-0001-7356-1683","affiliations":[{"raw_affiliation_string":"Department of Physics, Babes-Bolyai University, 400084 Cluj-Napoca, Romania","institution_ids":["https://openalex.org/I3125347698"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038398506","display_name":"M\u00e1ria Ercsey-Ravasz","orcid":"https://orcid.org/0000-0003-4428-9953"},"institutions":[{"id":"https://openalex.org/I3125347698","display_name":"Babe\u0219-Bolyai University","ror":"https://ror.org/02rmd1t30","country_code":"RO","type":"education","lineage":["https://openalex.org/I3125347698"]},{"id":"https://openalex.org/I4210141787","display_name":"Romanian Institute of Science and Technology","ror":"https://ror.org/04dchsd96","country_code":"RO","type":"nonprofit","lineage":["https://openalex.org/I4210141787"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"M\u00e1ria Ercsey-Ravasz","raw_affiliation_strings":["Department of Physics, Babes-Bolyai University, 400084 Cluj-Napoca, Romania","Network Science Lab, Transylvanian Institute of Neuroscience, 400157 Cluj-Napoca, Romania"],"raw_orcid":"https://orcid.org/0000-0003-4428-9953","affiliations":[{"raw_affiliation_string":"Department of Physics, Babes-Bolyai University, 400084 Cluj-Napoca, Romania","institution_ids":["https://openalex.org/I3125347698"]},{"raw_affiliation_string":"Network Science Lab, Transylvanian Institute of Neuroscience, 400157 Cluj-Napoca, Romania","institution_ids":["https://openalex.org/I4210141787"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5023524348","https://openalex.org/A5038398506"],"corresponding_institution_ids":["https://openalex.org/I3125347698","https://openalex.org/I4210141787"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.595,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.61710818,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"23","issue":"1","first_page":"103","last_page":"103"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.9914000034332275,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.9914000034332275,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9889000058174133,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9886000156402588,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.8985748291015625},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.6404827833175659},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.5737938284873962},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.5335007309913635},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5276414752006531},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4767538011074066},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4742133617401123},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.45618194341659546},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.4406471848487854},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.4310707449913025},{"id":"https://openalex.org/keywords/phase-space","display_name":"Phase space","score":0.42316144704818726},{"id":"https://openalex.org/keywords/complex-network","display_name":"Complex network","score":0.41712889075279236},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.4102162718772888},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3187599182128906},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14090684056282043},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12929224967956543},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.09116503596305847}],"concepts":[{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.8985748291015625},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.6404827833175659},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5737938284873962},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.5335007309913635},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5276414752006531},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4767538011074066},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4742133617401123},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.45618194341659546},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.4406471848487854},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.4310707449913025},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.42316144704818726},{"id":"https://openalex.org/C34947359","wikidata":"https://www.wikidata.org/wiki/Q665189","display_name":"Complex network","level":2,"score":0.41712889075279236},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4102162718772888},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3187599182128906},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14090684056282043},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12929224967956543},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.09116503596305847},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e23010103","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23010103","pdf_url":"https://www.mdpi.com/1099-4300/23/1/103/pdf?version=1611303693","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},{"id":"pmid:33445685","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33445685","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:b59d92e78ce24d1c85f2f4fc0a5ab197","is_oa":true,"landing_page_url":"https://doaj.org/article/b59d92e78ce24d1c85f2f4fc0a5ab197","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 23, Iss 1, p 103 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/23/1/103/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e23010103","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":"Entropy; Volume 23; Issue 1; Pages: 103","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:7828116","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7828116","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e23010103","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23010103","pdf_url":"https://www.mdpi.com/1099-4300/23/1/103/pdf?version=1611303693","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2336646951","display_name":null,"funder_award_id":"PN-III-P1-1.1-PD-2019-0742","funder_id":"https://openalex.org/F4320323983","funder_display_name":"Unitatea Executiva pentru Finantarea Invatamantului Superior, a Cercetarii, Dezvoltarii si Inovarii"},{"id":"https://openalex.org/G3003050846","display_name":null,"funder_award_id":"PN-III-P1-1.1-TE-2016-1457","funder_id":"https://openalex.org/F4320323983","funder_display_name":"Unitatea Executiva pentru Finantarea Invatamantului Superior, a Cercetarii, Dezvoltarii si Inovarii"},{"id":"https://openalex.org/G4112593687","display_name":null,"funder_award_id":"952096","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G6058054535","display_name":null,"funder_award_id":"PN-III-P1-1.1","funder_id":"https://openalex.org/F4320323983","funder_display_name":"Unitatea Executiva pentru Finantarea Invatamantului Superior, a Cercetarii, Dezvoltarii si Inovarii"},{"id":"https://openalex.org/G7688415803","display_name":null,"funder_award_id":"PN-III-P1-1","funder_id":"https://openalex.org/F4320323983","funder_display_name":"Unitatea Executiva pentru Finantarea Invatamantului Superior, a Cercetarii, Dezvoltarii si Inovarii"}],"funders":[{"id":"https://openalex.org/F4320315989","display_name":"National Authority for Scientific Research and Innovation","ror":null},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320323444","display_name":"Autoritatea National\u0103 pentru Cercetare Stiintific\u0103","ror":"https://ror.org/03padf885"},{"id":"https://openalex.org/F4320323983","display_name":"Unitatea Executiva pentru Finantarea Invatamantului Superior, a Cercetarii, Dezvoltarii si Inovarii","ror":"https://ror.org/01q7jq182"},{"id":"https://openalex.org/F4320336189","display_name":"Colegiul Consultativ pentru Cercetare-Dezvoltare \u015fi Inovare","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3120551547.pdf","grobid_xml":"https://content.openalex.org/works/W3120551547.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W580868470","https://openalex.org/W1871076392","https://openalex.org/W1966304312","https://openalex.org/W1985063305","https://openalex.org/W2000817338","https://openalex.org/W2001994500","https://openalex.org/W2007358085","https://openalex.org/W2010821195","https://openalex.org/W2019627326","https://openalex.org/W2032208242","https://openalex.org/W2036121390","https://openalex.org/W2049719481","https://openalex.org/W2109713924","https://openalex.org/W2125566231","https://openalex.org/W2141394518","https://openalex.org/W2167845354","https://openalex.org/W2297772255","https://openalex.org/W2395653583","https://openalex.org/W2474562813","https://openalex.org/W2485265736","https://openalex.org/W2486083357","https://openalex.org/W2537943564","https://openalex.org/W2563523061","https://openalex.org/W2734442794","https://openalex.org/W2899125647","https://openalex.org/W2939609801","https://openalex.org/W3006768132","https://openalex.org/W3098743667","https://openalex.org/W3100528154","https://openalex.org/W3100546788","https://openalex.org/W3101478121","https://openalex.org/W3124661333","https://openalex.org/W4233725098","https://openalex.org/W4235019172","https://openalex.org/W4235646468","https://openalex.org/W4239570095","https://openalex.org/W4242246215","https://openalex.org/W4300884679","https://openalex.org/W6722992161"],"related_works":["https://openalex.org/W1979229270","https://openalex.org/W2374600121","https://openalex.org/W2973136064","https://openalex.org/W3013851045","https://openalex.org/W2012691558","https://openalex.org/W2009385573","https://openalex.org/W1990019600","https://openalex.org/W2081531990","https://openalex.org/W5179970","https://openalex.org/W2037277714"],"abstract_inverted_index":{"The":[0],"combination":[1],"of":[2,31,38,69,74,81,137,157],"network":[3,47],"sciences,":[4],"nonlinear":[5],"dynamics":[6,52],"and":[7,14,34,63,118],"time":[8,103,117,120],"series":[9,104],"analysis":[10],"provides":[11],"novel":[12],"insights":[13],"analogies":[15],"between":[16,61],"the":[17,25,28,35,51,79,82,92,123,128,138,155],"different":[18],"approaches":[19],"to":[20,105,135,148],"complex":[21],"systems.":[22],"By":[23],"combining":[24],"considerations":[26],"behind":[27],"Lyapunov":[29,71,124,139],"exponent":[30],"dynamical":[32,121],"systems":[33,122],"average":[36],"entropy":[37],"transition":[39,107],"probabilities":[40],"for":[41,49,90,101],"Markov":[42],"chains,":[43],"we":[44,95],"introduce":[45],"a":[46,99,145],"measure":[48,72,125],"characterizing":[50],"on":[53,59,78],"state-transition":[54,130],"networks":[55,108,131],"with":[56],"special":[57],"focus":[58],"differentiating":[60],"chaotic":[62],"cyclic":[64],"modes.":[65],"One":[66],"important":[67],"property":[68],"this":[70],"consists":[73],"its":[75],"non-monotonous":[76],"dependence":[77],"cylicity":[80],"dynamics.":[83],"Motivated":[84],"by":[85,109],"providing":[86],"proper":[87],"use":[88],"cases":[89],"studying":[91],"new":[93],"measure,":[94],"also":[96],"lay":[97],"out":[98],"method":[100],"mapping":[102],"state":[106],"phase":[110],"space":[111],"coarse":[112],"graining.":[113],"Using":[114],"both":[115],"discrete":[116],"continuous":[119],"extracted":[126],"from":[127],"corresponding":[129],"exhibits":[132],"similar":[133],"behavior":[134],"that":[136],"exponent.":[140],"In":[141],"addition,":[142],"it":[143],"demonstrates":[144],"strong":[146],"sensitivity":[147],"boundary":[149],"crisis":[150],"suggesting":[151],"applicability":[152],"in":[153],"predicting":[154],"collapse":[156],"chaos.":[158]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}