{"id":"https://openalex.org/W3034619572","doi":"https://doi.org/10.1109/tnse.2020.3032117","title":"Nonlinear Control of Networked Dynamical Systems","display_name":"Nonlinear Control of Networked Dynamical Systems","publication_year":2020,"publication_date":"2020-10-21","ids":{"openalex":"https://openalex.org/W3034619572","doi":"https://doi.org/10.1109/tnse.2020.3032117","mag":"3034619572","pmid":"https://pubmed.ncbi.nlm.nih.gov/33997094"},"language":"en","primary_location":{"id":"doi:10.1109/tnse.2020.3032117","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnse.2020.3032117","pdf_url":null,"source":{"id":"https://openalex.org/S2484352698","display_name":"IEEE Transactions on Network Science and Engineering","issn_l":"2327-4697","issn":["2327-4697","2334-329X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Network Science and Engineering","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2006.05507","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044631633","display_name":"Megan Morrison","orcid":"https://orcid.org/0000-0002-3002-0585"},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]},{"id":"https://openalex.org/I4210138199","display_name":"University of Washington Applied Physics Laboratory","ror":"https://ror.org/03d17d270","country_code":"US","type":"facility","lineage":["https://openalex.org/I201448701","https://openalex.org/I4210138199"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Megan Morrison","raw_affiliation_strings":["Department of Applied Mathematics, University of Washington, Seattle, WA, 98195 USA","University of Washington ;"],"raw_orcid":"https://orcid.org/0000-0002-3002-0585","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Washington, Seattle, WA, 98195 USA","institution_ids":["https://openalex.org/I4210138199"]},{"raw_affiliation_string":"University of Washington ;","institution_ids":["https://openalex.org/I201448701"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083450863","display_name":"J. Nathan Kutz","orcid":"https://orcid.org/0000-0002-6004-2275"},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]},{"id":"https://openalex.org/I4210138199","display_name":"University of Washington Applied Physics Laboratory","ror":"https://ror.org/03d17d270","country_code":"US","type":"facility","lineage":["https://openalex.org/I201448701","https://openalex.org/I4210138199"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. Nathan Kutz","raw_affiliation_strings":["Department of Applied Mathematics, University of Washington, Seattle, WA, 98195 USA","University of Washington ;"],"raw_orcid":"https://orcid.org/0000-0002-6004-2275","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Washington, Seattle, WA, 98195 USA","institution_ids":["https://openalex.org/I4210138199"]},{"raw_affiliation_string":"University of Washington ;","institution_ids":["https://openalex.org/I201448701"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2045,"currency":"USD","value_usd":2045},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05508168,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"8","issue":"1","first_page":"174","last_page":"189"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.9991000294685364,"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":0.9991000294685364,"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/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":0.996999979019165,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.6208173632621765},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6182675957679749},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.56819748878479},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5368407964706421},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5185361504554749},{"id":"https://openalex.org/keywords/reachability","display_name":"Reachability","score":0.5146649479866028},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.5075134038925171},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.4748283326625824},{"id":"https://openalex.org/keywords/nonlinear-control","display_name":"Nonlinear control","score":0.4696832001209259},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.44420450925827026},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.42898592352867126},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3289400339126587},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.26052337884902954},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.23164039850234985},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.19353246688842773},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06811600923538208}],"concepts":[{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.6208173632621765},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6182675957679749},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.56819748878479},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5368407964706421},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5185361504554749},{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.5146649479866028},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.5075134038925171},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.4748283326625824},{"id":"https://openalex.org/C91581856","wikidata":"https://www.wikidata.org/wiki/Q2707001","display_name":"Nonlinear control","level":3,"score":0.4696832001209259},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.44420450925827026},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.42898592352867126},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3289400339126587},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.26052337884902954},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.23164039850234985},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.19353246688842773},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06811600923538208},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1109/tnse.2020.3032117","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnse.2020.3032117","pdf_url":null,"source":{"id":"https://openalex.org/S2484352698","display_name":"IEEE Transactions on Network Science and Engineering","issn_l":"2327-4697","issn":["2327-4697","2334-329X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Network Science and Engineering","raw_type":"journal-article"},{"id":"pmid:33997094","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33997094","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":"IEEE transactions on network science and engineering","raw_type":"Journal Article"},{"id":"pmh:oai:arXiv.org:2006.05507","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2006.05507","pdf_url":"https://arxiv.org/pdf/2006.05507","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:pubmedcentral.nih.gov:8117950","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/8117950","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Trans Netw Sci Eng","raw_type":"Text"},{"id":"mag:3034619572","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2006.05507.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2006.05507","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2006.05507","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2006.05507","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2006.05507","pdf_url":"https://arxiv.org/pdf/2006.05507","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1072749480","display_name":null,"funder_award_id":"FA9550-17","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G1523888516","display_name":null,"funder_award_id":"FA9550-","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G260750634","display_name":null,"funder_award_id":"FA9550-17-1","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G5754427093","display_name":null,"funder_award_id":"T32 LM012419","funder_id":"https://openalex.org/F4320337372","funder_display_name":"U.S. National Library of Medicine"},{"id":"https://openalex.org/G6526921895","display_name":null,"funder_award_id":"FA9550-17-1-0329","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G8090702242","display_name":"University of Washington PhD Training in Big Data for Genomics and Neuroscience","funder_award_id":"5t32lm012419-04","funder_id":"https://openalex.org/F4320332161","funder_display_name":"National Institutes of Health"},{"id":"https://openalex.org/G8986540951","display_name":null,"funder_award_id":"W911NF1910291","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"}],"funders":[{"id":"https://openalex.org/F4320332161","display_name":"National Institutes of Health","ror":"https://ror.org/01cwqze88"},{"id":"https://openalex.org/F4320337372","display_name":"U.S. National Library of Medicine","ror":"https://ror.org/0060t0j89"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":102,"referenced_works":["https://openalex.org/W40048283","https://openalex.org/W71430541","https://openalex.org/W616193750","https://openalex.org/W1484739396","https://openalex.org/W1485467598","https://openalex.org/W1515138319","https://openalex.org/W1565761872","https://openalex.org/W1576347883","https://openalex.org/W1579520422","https://openalex.org/W1599936794","https://openalex.org/W1723433682","https://openalex.org/W1868105705","https://openalex.org/W1888005072","https://openalex.org/W1963942260","https://openalex.org/W1964099314","https://openalex.org/W1972963245","https://openalex.org/W1975900269","https://openalex.org/W1977738976","https://openalex.org/W1985841281","https://openalex.org/W1985940938","https://openalex.org/W1989276588","https://openalex.org/W1989915587","https://openalex.org/W1996901117","https://openalex.org/W1997228791","https://openalex.org/W1999034136","https://openalex.org/W2001428612","https://openalex.org/W2003334682","https://openalex.org/W2007673294","https://openalex.org/W2009375605","https://openalex.org/W2013468174","https://openalex.org/W2022083463","https://openalex.org/W2029030701","https://openalex.org/W2041985017","https://openalex.org/W2046643693","https://openalex.org/W2054316680","https://openalex.org/W2061191702","https://openalex.org/W2086126894","https://openalex.org/W2089876099","https://openalex.org/W2097722513","https://openalex.org/W2100495367","https://openalex.org/W2111167674","https://openalex.org/W2112796928","https://openalex.org/W2117950425","https://openalex.org/W2121775913","https://openalex.org/W2128084896","https://openalex.org/W2130607429","https://openalex.org/W2132796361","https://openalex.org/W2134759932","https://openalex.org/W2135076964","https://openalex.org/W2137855502","https://openalex.org/W2140684369","https://openalex.org/W2148301044","https://openalex.org/W2149158842","https://openalex.org/W2152896489","https://openalex.org/W2156718197","https://openalex.org/W2161728228","https://openalex.org/W2165616177","https://openalex.org/W2167215970","https://openalex.org/W2171281863","https://openalex.org/W2233438185","https://openalex.org/W2239232218","https://openalex.org/W2525748878","https://openalex.org/W2582771730","https://openalex.org/W2688047394","https://openalex.org/W2736746078","https://openalex.org/W2752422601","https://openalex.org/W2768748954","https://openalex.org/W2777987555","https://openalex.org/W2806254974","https://openalex.org/W2915622878","https://openalex.org/W2947024452","https://openalex.org/W2947085993","https://openalex.org/W2950967261","https://openalex.org/W2963288853","https://openalex.org/W2963575288","https://openalex.org/W2964145209","https://openalex.org/W2964265215","https://openalex.org/W2970917037","https://openalex.org/W2981906852","https://openalex.org/W2994929914","https://openalex.org/W2996711689","https://openalex.org/W3001894473","https://openalex.org/W3002444177","https://openalex.org/W3099165741","https://openalex.org/W3100769368","https://openalex.org/W3101466225","https://openalex.org/W3105705953","https://openalex.org/W3112281758","https://openalex.org/W4210968171","https://openalex.org/W4236990395","https://openalex.org/W4292510839","https://openalex.org/W4299690715","https://openalex.org/W4320800818","https://openalex.org/W6601657841","https://openalex.org/W6634556092","https://openalex.org/W6677302490","https://openalex.org/W6682044371","https://openalex.org/W6682755970","https://openalex.org/W6684563725","https://openalex.org/W6763097295","https://openalex.org/W6773225017","https://openalex.org/W6785731190"],"related_works":["https://openalex.org/W3094227968","https://openalex.org/W1641819801","https://openalex.org/W2242889413","https://openalex.org/W2207062742","https://openalex.org/W2751343598","https://openalex.org/W2014382681","https://openalex.org/W2998908629","https://openalex.org/W2627088983","https://openalex.org/W2567535370","https://openalex.org/W2910531493","https://openalex.org/W2791282573","https://openalex.org/W3156311101","https://openalex.org/W3204007682","https://openalex.org/W3036748946","https://openalex.org/W2942918465","https://openalex.org/W3035427370","https://openalex.org/W2777417212","https://openalex.org/W2969047780","https://openalex.org/W3098780444"],"abstract_inverted_index":{"We":[0,157,182],"develop":[1],"a":[2,36,39,86,121,128],"principled":[3],"mathematical":[4],"framework":[5],"for":[6,57,120,188],"controlling":[7],"nonlinear,":[8],"networked":[9,50],"dynamical":[10,88],"systems.":[11],"Our":[12],"method":[13,43],"integrates":[14],"dimensionality":[15],"reduction,":[16],"bifurcation":[17,104],"theory,":[18],"and":[19,154,195],"emerging":[20],"model":[21],"discovery":[22],"tools":[23],"to":[24,34,38,84,90,102,106,149],"find":[25,107],"low-dimensional":[26,166],"subspaces":[27],"where":[28],"feed-forward":[29],"control":[30,61,111,142,155,161,171,186],"can":[31,126,144],"be":[32,145],"used":[33,83],"manipulate":[35],"system":[37,67,89],"desired":[40,117],"outcome.":[41,123],"The":[42,74,140],"leverages":[44],"the":[45,58,66,91,94,116,134,150,179],"fact":[46],"that":[47,63,113,175],"many":[48,53],"high-dimensional":[49,152,189,193],"systems":[51,190],"have":[52],"fixed":[54,72,130,136,180],"points,":[55],"allowing":[56],"computation":[59],"of":[60,71,77,109],"signals":[62,112,143,172],"will":[64,114],"move":[65],"between":[68,178],"any":[69],"pair":[70],"points.":[73,181],"sparse":[75],"identification":[76],"nonlinear":[78,87,160],"dynamics":[79],"(SINDy)":[80],"algorithm":[81],"is":[82],"fit":[85],"evolution":[92],"on":[93,163,191],"dominant,":[95],"low-rank":[96],"subspace.":[97],"This":[98],"then":[99,183],"allows":[100],"us":[101],"use":[103],"theory":[105],"collections":[108],"constant":[110],"produce":[115],"objective":[118],"path":[119],"prescribed":[122],"Specifically,":[124],"we":[125],"destabilize":[127],"given":[129],"point":[131,137],"while":[132],"making":[133],"target":[135],"an":[138],"attractor.":[139],"discovered":[141],"easily":[146],"projected":[147],"back":[148],"original":[151],"state":[153],"space.":[156],"illustrate":[158],"our":[159,185],"procedure":[162,187],"established":[164],"bistable,":[165],"biological":[167],"systems,":[168],"showing":[169],"how":[170],"are":[173],"found":[174],"generate":[176],"switches":[177],"demonstrate":[184],"random":[192],"networks":[194],"Hopfield":[196],"memory":[197],"networks.":[198]},"counts_by_year":[],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2025-10-10T00:00:00"}