{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T18:59:47Z","timestamp":1790881187358,"version":"4.1.0"},"reference-count":68,"publisher":"American Physical Society (APS)","issue":"1","license":[{"start":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T00:00:00Z","timestamp":1783468800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/link.aps.org\/licenses\/aps-default-license"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12572009"],"award-info":[{"award-number":["12572009"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12072128"],"award-info":[{"award-number":["12072128"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. E"],"accepted":{"date-parts":[[2026,6,16]]},"DOI":"10.1103\/chvg-gfy8","type":"journal-article","created":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T15:02:52Z","timestamp":1781622172000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Model-free analysis of complex systems using delayed-feedback echo state network"],"prefix":"10.1103","volume":"114","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-4927-6572","authenticated-orcid":true,"given":"Wenjing","family":"Guo","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00js3aw79","id-type":"ROR","asserted-by":"publisher"}],"name":"Jilin University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-3904-7347","authenticated-orcid":true,"given":"Shuang","family":"Li","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00js3aw79","id-type":"ROR","asserted-by":"publisher"}],"name":"Jilin University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-5830-8737","authenticated-orcid":true,"given":"Jianming","family":"Liu","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01xt2dr21","id-type":"ROR","asserted-by":"publisher"}],"name":"China University of Mining and Technology"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9656-9258","authenticated-orcid":true,"given":"Eric","family":"Li","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03z28gk75","id-type":"ROR","asserted-by":"publisher"}],"name":"Teesside University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0691-8248","authenticated-orcid":true,"given":"Xu","family":"Xu","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00js3aw79","id-type":"ROR","asserted-by":"publisher"}],"name":"Jilin University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"16","published-online":{"date-parts":[[2026,7,8]]},"reference":[{"key":"chvg-gfy8Cc1R1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1517384113","type":"journal-article"},{"key":"chvg-gfy8Cc2R1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1906995116","type":"journal-article"},{"key":"chvg-gfy8Cc3R1","doi-asserted-by":"publisher","DOI":"10.1126\/science.aaa8415","type":"journal-article"},{"key":"chvg-gfy8Cc4R1","doi-asserted-by":"publisher","DOI":"10.1145\/2347736.2347755","type":"journal-article"},{"key":"chvg-gfy8Cc5R1","doi-asserted-by":"publisher","DOI":"10.1038\/nature14539","type":"journal-article"},{"key":"chvg-gfy8Cc6R1","doi-asserted-by":"publisher","DOI":"10.1145\/3065386","type":"journal-article"},{"key":"chvg-gfy8Cc7R1","doi-asserted-by":"publisher","DOI":"10.1136\/amiajnl-2011-000464","type":"journal-article"},{"key":"chvg-gfy8Cc8R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2015.02.029","type":"journal-article"},{"key":"chvg-gfy8Cc9R1","doi-asserted-by":"publisher","DOI":"10.1111\/joes.12429","type":"journal-article"},{"key":"chvg-gfy8Cc10R1","unstructured":"H. Jaeger, The \u201cecho state\u201d approach to analysing and training recurrent neural networks-with an erratum note, GMD Technical Report No. 148, German National Research Center for Information Technology, Bonn, Germany, 2001.","type":"other"},{"key":"chvg-gfy8Cc11R1","doi-asserted-by":"publisher","DOI":"10.32604\/jai.2024.054314","type":"journal-article"},{"key":"chvg-gfy8Cc12R1","volume-title":"ICASSP 2021-2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)","author":"L. Sun","year":"2021","type":"conference-proceedings"},{"key":"chvg-gfy8Cc13R1","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2021.3107858","type":"journal-article"},{"key":"chvg-gfy8Cc14R1","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-022-07410-2","type":"journal-article"},{"key":"chvg-gfy8Cc15R1","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2020.3001377","type":"journal-article"},{"key":"chvg-gfy8Cc16R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2021.107314","type":"journal-article"},{"key":"chvg-gfy8Cc17R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2023.10.041","type":"journal-article"},{"key":"chvg-gfy8Cc18R1","volume-title":"2021 International Conference on Neuromorphic Computing (ICNC)","author":"J. Sun","year":"2021","type":"conference-proceedings"},{"key":"chvg-gfy8Cc19R1","volume-title":"2021 IEEE International Midwest Symposium on Circuits and Systems (MWSCAS)","author":"S.\u00a0D. Gardner","year":"2021","type":"book"},{"key":"chvg-gfy8Cc20R1","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2015.2479117","type":"journal-article"},{"key":"chvg-gfy8Cc21R1","doi-asserted-by":"publisher","DOI":"10.1063\/5.0049911","type":"journal-article"},{"key":"chvg-gfy8Cc22R1","volume-title":"2016 International Joint Conference on Neural Networks (IJCNN)","author":"A. Souahlia","year":"2016","type":"conference-proceedings"},{"key":"chvg-gfy8Cc23R1","doi-asserted-by":"publisher","DOI":"10.1002\/cpe.5719","type":"journal-article"},{"key":"chvg-gfy8Cc24R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.compbiomed.2019.05.024","type":"journal-article"},{"key":"chvg-gfy8Cc25R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.mlwa.2022.100300","type":"journal-article"},{"key":"chvg-gfy8Cc26R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.109.024227","type":"journal-article"},{"key":"chvg-gfy8Cc27R1","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-023-09271-9","type":"journal-article"},{"key":"chvg-gfy8Cc28R1","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-024-09448-4","type":"journal-article"},{"key":"chvg-gfy8Cc29R1","doi-asserted-by":"publisher","DOI":"10.1126\/science.1091277","type":"journal-article"},{"key":"chvg-gfy8Cc30R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.120.024102","type":"journal-article"},{"key":"chvg-gfy8Cc31R1","doi-asserted-by":"publisher","DOI":"10.1063\/5.0119963","type":"journal-article"},{"key":"chvg-gfy8Cc32R1","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-025-10942-6","type":"journal-article"},{"key":"chvg-gfy8Cc33R1","doi-asserted-by":"publisher","DOI":"10.1103\/7pv3-8792","type":"journal-article"},{"key":"chvg-gfy8Cc34R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2007.04.016","type":"journal-article"},{"key":"chvg-gfy8Cc35R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2021.104229","type":"journal-article"},{"key":"chvg-gfy8Cc36R1","doi-asserted-by":"publisher","DOI":"10.1140\/epjb\/s10051-022-00280-6","type":"journal-article"},{"key":"chvg-gfy8Cc37R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.109.064210","type":"journal-article"},{"key":"chvg-gfy8Cc38R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2016.12.089","type":"journal-article"},{"key":"chvg-gfy8Cc39R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2015.12.013","type":"journal-article"},{"key":"chvg-gfy8Cc40R1","unstructured":"H. Jaeger, Short term memory in echo state networks, GMD Technical Report No. 152, German National Research Center for Information Technology, Bonn, Germany, 2002.","type":"other"},{"key":"chvg-gfy8Cc41R1","doi-asserted-by":"publisher","DOI":"10.1007\/s12043-017-1505-x","type":"journal-article"},{"key":"chvg-gfy8Cc42R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2012.09.003","type":"journal-article"},{"key":"chvg-gfy8Cc43R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2013.06.001","type":"journal-article"},{"key":"chvg-gfy8Cc44R1","doi-asserted-by":"publisher","DOI":"10.1063\/5.0200898","type":"journal-article"},{"key":"chvg-gfy8Cc45R1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127424500251","type":"journal-article"},{"key":"chvg-gfy8Cc46R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.104.014205","type":"journal-article"},{"key":"chvg-gfy8Cc47R1","doi-asserted-by":"publisher","DOI":"10.1063\/5.0065617","type":"journal-article"},{"key":"chvg-gfy8Cc48R1","volume-title":"Proceedings of the 26th International Conference on Neural Information Processing Systems - Volume 2","author":"J. Snoek","year":"2016","type":"conference-proceedings"},{"key":"chvg-gfy8Cc49R1","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-016-2474-6","type":"journal-article"},{"key":"chvg-gfy8Cc50R1","doi-asserted-by":"publisher","DOI":"10.1143\/PTP.55.356","type":"journal-article"},{"key":"chvg-gfy8Cc51R1","doi-asserted-by":"publisher","DOI":"10.1016\/0094-5765(77)90097-2","type":"journal-article"},{"key":"chvg-gfy8Cc52R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2020.06.020","type":"journal-article"},{"key":"chvg-gfy8Cc53R1","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2017.0844","type":"journal-article"},{"key":"chvg-gfy8Cc54R1","unstructured":"COMSOL multiphysics\u00ae v. 6.1, https:\/\/www.comsol.com.","type":"other"},{"key":"chvg-gfy8Cc55R1","doi-asserted-by":"publisher","DOI":"10.52202\/068431-1220","type":"journal-article"},{"key":"chvg-gfy8Cc56R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2025.118125","type":"journal-article"},{"key":"chvg-gfy8Cc57R1","first-page":"6571","type":"journal-article","volume":"31","author":"R.\u00a0T.\u00a0Q. Chen","year":"2018","journal-title":"Adv. Neural Inf. Proc. Syst."},{"key":"chvg-gfy8Cc58R1","doi-asserted-by":"publisher","DOI":"10.1140\/epjs\/s11734-021-00371-y","type":"journal-article"},{"key":"chvg-gfy8Cc59R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.3.013090","type":"journal-article"},{"key":"chvg-gfy8Cc60R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.67.026603","type":"journal-article"},{"key":"chvg-gfy8Cc61R1","doi-asserted-by":"publisher","DOI":"10.1364\/OE.23.012823","type":"journal-article"},{"key":"chvg-gfy8Cc62R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.patrec.2005.10.010","type":"journal-article"},{"key":"chvg-gfy8Cc63R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.5010300","type":"journal-article"},{"key":"chvg-gfy8Cc64R1","doi-asserted-by":"publisher","DOI":"10.1063\/5.0028993","type":"journal-article"},{"key":"chvg-gfy8Cc65R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-024-81880-3","type":"journal-article"},{"key":"chvg-gfy8Cc66R1","doi-asserted-by":"publisher","DOI":"10.1063\/5.0272793","type":"journal-article"},{"key":"chvg-gfy8Cc67R1","doi-asserted-by":"publisher","DOI":"10.3934\/dcdss.2020352","type":"journal-article"},{"key":"chvg-gfy8Cc68R1","volume-title":"International Conference on Intelligent Data Engineering and Automated Learning","author":"S. Iacob","year":"2022","type":"conference-proceedings"}],"container-title":["Physical Review E"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.aps.org\/article\/10.1103\/chvg-gfy8","content-type":"unspecified","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/harvest.aps.org\/v2\/journals\/articles\/10.1103\/chvg-gfy8\/fulltext","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T18:02:46Z","timestamp":1790877766000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.aps.org\/doi\/10.1103\/chvg-gfy8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7,8]]},"references-count":68,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,7]]}},"URL":"https:\/\/doi.org\/10.1103\/chvg-gfy8","relation":{},"ISSN":["2470-0045","2470-0053"],"issn-type":[{"value":"2470-0045","type":"print"},{"value":"2470-0053","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7,8]]},"assertion":[{"value":"2025-09-24","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"\u00a92026 American Physical Society. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright_statement","label":"Copyright statement","group":{"name":"copyright","label":"copyright"}},{"value":"2026","name":"copyright_year","label":"Copyright year","group":{"name":"copyright","label":"copyright"}},{"value":"American Physical Society","name":"copyright_holder","label":"Copyright holder","group":{"name":"copyright","label":"copyright"}}],"article-number":"014204"}}