{"id":"https://openalex.org/W2766422444","doi":"https://doi.org/10.1137/16m1092581","title":"Lyapunov-Based Stability and Construction of Lyapunov Functions for Boolean Networks","display_name":"Lyapunov-Based Stability and Construction of Lyapunov Functions for Boolean Networks","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2766422444","doi":"https://doi.org/10.1137/16m1092581","mag":"2766422444"},"language":"en","primary_location":{"id":"doi:10.1137/16m1092581","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1092581","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100453276","display_name":"Haitao Li","orcid":"https://orcid.org/0000-0001-5322-5375"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Haitao Li","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100784464","display_name":"Yuzhen Wang","orcid":"https://orcid.org/0000-0003-1299-4519"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yuzhen Wang","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100453276"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.6025,"has_fulltext":false,"cited_by_count":115,"citation_normalized_percentile":{"value":0.981107,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"55","issue":"6","first_page":"3437","last_page":"3457"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9998999834060669,"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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9732999801635742,"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"}},{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9677000045776367,"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/lyapunov-function","display_name":"Lyapunov function","score":0.8467459678649902},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7854679822921753},{"id":"https://openalex.org/keywords/lyapunov-redesign","display_name":"Lyapunov redesign","score":0.7604845762252808},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.7389576435089111},{"id":"https://openalex.org/keywords/lyapunov-optimization","display_name":"Lyapunov optimization","score":0.7011078596115112},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.48644042015075684},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.46823447942733765},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.46655386686325073},{"id":"https://openalex.org/keywords/control-lyapunov-function","display_name":"Control-Lyapunov function","score":0.430219829082489},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3598778545856476},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32587286829948425},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.21526503562927246},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14680486917495728},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.10298028588294983},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.07838767766952515},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06450352072715759}],"concepts":[{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.8467459678649902},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7854679822921753},{"id":"https://openalex.org/C37935115","wikidata":"https://www.wikidata.org/wiki/Q6707085","display_name":"Lyapunov redesign","level":4,"score":0.7604845762252808},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.7389576435089111},{"id":"https://openalex.org/C101403955","wikidata":"https://www.wikidata.org/wiki/Q6707083","display_name":"Lyapunov optimization","level":5,"score":0.7011078596115112},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.48644042015075684},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.46823447942733765},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.46655386686325073},{"id":"https://openalex.org/C201030206","wikidata":"https://www.wikidata.org/wiki/Q5165805","display_name":"Control-Lyapunov function","level":5,"score":0.430219829082489},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3598778545856476},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32587286829948425},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.21526503562927246},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14680486917495728},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.10298028588294983},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.07838767766952515},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06450352072715759},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/16m1092581","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1092581","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3020716557","display_name":null,"funder_award_id":"61503225","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7198419683","display_name":null,"funder_award_id":"ZR2015FQ003","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"},{"id":"https://openalex.org/G7995498719","display_name":null,"funder_award_id":"JQ201613","funder_id":"https://openalex.org/F4320334910","funder_display_name":"Distinguished Middle-Aged and Young Scientist Encourage and Reward Foundation of Shandong Province"},{"id":"https://openalex.org/G8795705117","display_name":null,"funder_award_id":"61374065","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320324174","display_name":"Natural Science Foundation of Shandong Province","ror":null},{"id":"https://openalex.org/F4320334910","display_name":"Distinguished Middle-Aged and Young Scientist Encourage and Reward Foundation of Shandong Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W940409914","https://openalex.org/W1535322767","https://openalex.org/W1910803460","https://openalex.org/W1971224531","https://openalex.org/W1971318969","https://openalex.org/W1991720013","https://openalex.org/W2004239486","https://openalex.org/W2008275926","https://openalex.org/W2020196141","https://openalex.org/W2024273375","https://openalex.org/W2030235975","https://openalex.org/W2030772003","https://openalex.org/W2033041501","https://openalex.org/W2041443351","https://openalex.org/W2045077417","https://openalex.org/W2046921524","https://openalex.org/W2053019692","https://openalex.org/W2053648336","https://openalex.org/W2062974796","https://openalex.org/W2065949669","https://openalex.org/W2077895748","https://openalex.org/W2082427151","https://openalex.org/W2088929609","https://openalex.org/W2090882632","https://openalex.org/W2095701698","https://openalex.org/W2101408219","https://openalex.org/W2113609870","https://openalex.org/W2118467699","https://openalex.org/W2118741873","https://openalex.org/W2121235966","https://openalex.org/W2136433622","https://openalex.org/W2149869214","https://openalex.org/W2160904474","https://openalex.org/W2168808496","https://openalex.org/W2260463403","https://openalex.org/W2267936660","https://openalex.org/W2290618319","https://openalex.org/W2297307567","https://openalex.org/W2344660126","https://openalex.org/W2397970027","https://openalex.org/W2429265837","https://openalex.org/W2435595704","https://openalex.org/W2565953397"],"related_works":["https://openalex.org/W3217133416","https://openalex.org/W2383986032","https://openalex.org/W2349796700","https://openalex.org/W1975178315","https://openalex.org/W2534107666","https://openalex.org/W1970635650","https://openalex.org/W2496188264","https://openalex.org/W3194517843","https://openalex.org/W2126112326","https://openalex.org/W2588600327"],"abstract_inverted_index":{"This":[0],"paper":[1,178],"investigates":[2],"the":[3,8,28,53,70,75,115,122,145,152,158,172],"Lyapunov-based":[4,86],"stability":[5,87,159],"analysis":[6,160],"and":[7,17,52,102,114,129,139],"construction":[9],"of":[10,22,31,47,55,77,124,161,167],"Lyapunov":[11,23,40,57,78,98,132],"functions":[12,49,58,79,126],"for":[13,25,42,80,100,106,144],"Boolean":[14,163],"networks":[15],"(BNs)":[16],"establishes":[18],"a":[19,39,66,97,111,118,130,137],"new":[20,173],"framework":[21],"theory":[24],"BNs":[26,101],"via":[27],"semitensor":[29],"product":[30],"matrices.":[32],"First,":[33],"we":[34,92],"study":[35,93,166],"how":[36,94],"to":[37,95,157],"define":[38],"function":[41,68,99],"BNs.":[43],"A":[44],"proper":[45,71],"form":[46,72],"pseudo-Boolean":[48,67],"is":[50,59,63,110,117,127],"found,":[51],"concept":[54],"(strict-)":[56],"thus":[60],"given.":[61],"It":[62],"shown":[64],"that":[65,171],"in":[69,176],"can":[73],"play":[74],"role":[76],"BNs,":[81],"based":[82],"on":[83],"which":[84],"several":[85],"results":[88,154],"are":[89,142,155],"obtained.":[90],"Second,":[91],"construct":[96],"propose":[103],"two":[104],"methods":[105],"this":[107,177],"problem:":[108],"one":[109],"definition-based":[112],"method,":[113],"other":[116],"structure-based":[119],"one.":[120],"Third,":[121],"existence":[123],"strict-Lyapunov":[125],"studied,":[128],"converse":[131],"theorem":[133],"as":[134,136,149],"well":[135],"necessary":[138],"sufficient":[140],"condition":[141],"obtained":[143,153],"asymptotical":[146],"stability.":[147],"Finally,":[148],"an":[150],"application,":[151],"applied":[156],"switched":[162],"networks.":[164],"The":[165],"illustrative":[168],"examples":[169],"shows":[170],"results/methods":[174],"proposed":[175],"work":[179],"very":[180],"well.":[181]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":24},{"year":2019,"cited_by_count":27},{"year":2018,"cited_by_count":16},{"year":2017,"cited_by_count":1}],"updated_date":"2026-03-17T09:09:15.849793","created_date":"2025-10-10T00:00:00"}