{"id":"https://openalex.org/W791415376","doi":"https://doi.org/10.1007/978-3-662-47221-7_5","title":"Effect of Graph Structure on the Limit Sets of Threshold Dynamical Systems","display_name":"Effect of Graph Structure on the Limit Sets of Threshold Dynamical Systems","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W791415376","doi":"https://doi.org/10.1007/978-3-662-47221-7_5","mag":"791415376"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-662-47221-7_5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-662-47221-7_5","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://inria.hal.science/hal-01442482","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019703184","display_name":"Abhijin Adiga","orcid":"https://orcid.org/0000-0002-9770-034X"},"institutions":[{"id":"https://openalex.org/I859038795","display_name":"Virginia Tech","ror":"https://ror.org/02smfhw86","country_code":"US","type":"education","lineage":["https://openalex.org/I859038795"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Abhijin Adiga","raw_affiliation_strings":["Network Dynamics and Simulation Science Laboratory, VBI, Virginia Tech, Blacksburg, USA"],"affiliations":[{"raw_affiliation_string":"Network Dynamics and Simulation Science Laboratory, VBI, Virginia Tech, Blacksburg, USA","institution_ids":["https://openalex.org/I859038795"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006412870","display_name":"Chris J. Kuhlman","orcid":"https://orcid.org/0000-0002-9368-2156"},"institutions":[{"id":"https://openalex.org/I859038795","display_name":"Virginia Tech","ror":"https://ror.org/02smfhw86","country_code":"US","type":"education","lineage":["https://openalex.org/I859038795"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chris J. Kuhlman","raw_affiliation_strings":["Network Dynamics and Simulation Science Laboratory, VBI, Virginia Tech, Blacksburg, USA"],"affiliations":[{"raw_affiliation_string":"Network Dynamics and Simulation Science Laboratory, VBI, Virginia Tech, Blacksburg, USA","institution_ids":["https://openalex.org/I859038795"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079309664","display_name":"Henning Mortveit","orcid":"https://orcid.org/0000-0003-3363-2947"},"institutions":[{"id":"https://openalex.org/I859038795","display_name":"Virginia Tech","ror":"https://ror.org/02smfhw86","country_code":"US","type":"education","lineage":["https://openalex.org/I859038795"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Henning S. Mortveit","raw_affiliation_strings":["Department of Mathematics, Virginia Tech, Blacksburg, USA","Network Dynamics and Simulation Science Laboratory, VBI, Virginia Tech, Blacksburg, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Virginia Tech, Blacksburg, USA","institution_ids":["https://openalex.org/I859038795"]},{"raw_affiliation_string":"Network Dynamics and Simulation Science Laboratory, VBI, Virginia Tech, Blacksburg, USA","institution_ids":["https://openalex.org/I859038795"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101891511","display_name":"Sichao Wu","orcid":"https://orcid.org/0000-0003-2171-6211"},"institutions":[{"id":"https://openalex.org/I859038795","display_name":"Virginia Tech","ror":"https://ror.org/02smfhw86","country_code":"US","type":"education","lineage":["https://openalex.org/I859038795"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sichao Wu","raw_affiliation_strings":["Network Dynamics and Simulation Science Laboratory, VBI, Virginia Tech, Blacksburg, USA"],"affiliations":[{"raw_affiliation_string":"Network Dynamics and Simulation Science Laboratory, VBI, Virginia Tech, Blacksburg, USA","institution_ids":["https://openalex.org/I859038795"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5019703184"],"corresponding_institution_ids":["https://openalex.org/I859038795"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.02729427,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"59","last_page":"70"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"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"}},"topics":[{"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9740999937057495,"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":0.9656999707221985,"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/attractor","display_name":"Attractor","score":0.581608772277832},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5622302293777466},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.5544191002845764},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5517565011978149},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.5345743298530579},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5282235145568848},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5152357220649719},{"id":"https://openalex.org/keywords/directed-graph","display_name":"Directed graph","score":0.4576725959777832},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4189401865005493},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3845507502555847},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33773982524871826},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.30395007133483887}],"concepts":[{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.581608772277832},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5622302293777466},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.5544191002845764},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5517565011978149},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.5345743298530579},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5282235145568848},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5152357220649719},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.4576725959777832},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4189401865005493},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3845507502555847},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33773982524871826},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.30395007133483887},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/978-3-662-47221-7_5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-662-47221-7_5","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:HAL:hal-01442482v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-01442482","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"21st Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA), Jun 2015, Turku, Finland. pp.59-70, ⟨10.1007/978-3-662-47221-7_5⟩","raw_type":"Conference papers"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-01442482v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-01442482","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"21st Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA), Jun 2015, Turku, Finland. pp.59-70, ⟨10.1007/978-3-662-47221-7_5⟩","raw_type":"Conference papers"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W122080237","https://openalex.org/W621998161","https://openalex.org/W1789344111","https://openalex.org/W1971224531","https://openalex.org/W1991079360","https://openalex.org/W1992901827","https://openalex.org/W2041157860","https://openalex.org/W2042210880","https://openalex.org/W2065909799","https://openalex.org/W2079434400","https://openalex.org/W2092522621","https://openalex.org/W2402371301","https://openalex.org/W2483473095","https://openalex.org/W2798588639","https://openalex.org/W2959792658"],"related_works":["https://openalex.org/W2960434112","https://openalex.org/W3049714198","https://openalex.org/W2036805113","https://openalex.org/W2592279130","https://openalex.org/W2049158118","https://openalex.org/W2083968322","https://openalex.org/W2070724789","https://openalex.org/W4382985020","https://openalex.org/W1973339055","https://openalex.org/W3190612612"],"abstract_inverted_index":{"We":[0,117,137],"study":[1,103],"the":[2,15,19,26,32,48,86,105,110,123,128],"attractor":[3],"structure":[4,108,113,125],"of":[5,18,52,68,88,114],"standard":[6],"block-sequential":[7,13,53,89,115],"threshold":[8,62,90],"dynamical":[9],"systems.":[10,116],"In":[11],"a":[12,119],"update,":[14],"vertex":[16],"set":[17],"graph":[20,107,124,142],"is":[21],"partitioned":[22],"into":[23],"blocks,":[24],"and":[25,57,82],"blocks":[27],"are":[28,37,42],"updated":[29,38],"sequentially":[30],"while":[31],"vertices":[33],"within":[34],"each":[35],"block":[36],"in":[39],"parallel.":[40,59],"There":[41],"several":[43,140],"notable":[44],"previous":[45],"results":[46],"concerning":[47],"two":[49],"extreme":[50],"cases":[51],"update:":[54],"(i)":[55],"sequential":[56,73],"(ii)":[58],"While":[60],"parallel":[61],"systems":[63,74,91],"can":[64,75],"have":[65,76,93],"limit":[66,96,111,135],"cycles":[67],"length":[69],"at":[70],"most":[71],"two,":[72],"only":[77,131],"fixed":[78,132],"points.":[79],"However,":[80],"Goles":[81],"Montealegre":[83],"[5]":[84],"showed":[85],"existence":[87],"that":[92,127,144],"arbitrarily":[94],"long":[95],"cycles.":[97,136],"Motivated":[98],"by":[99],"this":[100,146],"result,":[101],"we":[102],"how":[104],"underlying":[106],"influences":[109],"cycle":[112],"derive":[118],"sufficient":[120],"condition":[121],"on":[122],"so":[126],"system":[129],"has":[130],"points":[133],"as":[134],"also":[138],"identify":[139],"well-known":[141],"families":[143],"satisfy":[145],"condition.":[147]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}