{"id":"https://openalex.org/W4380483295","doi":"https://doi.org/10.1137/22m1489502","title":"Synchronization of Coupled Phase Oscillators with Stochastic Disturbances and the Cycle Space of the Graph","display_name":"Synchronization of Coupled Phase Oscillators with Stochastic Disturbances and the Cycle Space of the Graph","publication_year":2023,"publication_date":"2023-06-13","ids":{"openalex":"https://openalex.org/W4380483295","doi":"https://doi.org/10.1137/22m1489502"},"language":"en","primary_location":{"id":"doi:10.1137/22m1489502","is_oa":true,"landing_page_url":"https://doi.org/10.1137/22m1489502","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1137/22m1489502","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083836421","display_name":"Kaihua Xi","orcid":"https://orcid.org/0000-0003-2606-9543"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kaihua Xi","raw_affiliation_strings":["School of Mathematics, Shandong University, Jinan 250100, Shandong Province, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Shandong University, Jinan 250100, Shandong Province, China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100422334","display_name":"Zhen Wang","orcid":"https://orcid.org/0000-0002-4553-4976"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhen Wang","raw_affiliation_strings":["School of Mathematics, Shandong University, Jinan 250100, Shandong Province, China"],"raw_orcid":"https://orcid.org/0000-0002-4553-4976","affiliations":[{"raw_affiliation_string":"School of Mathematics, Shandong University, Jinan 250100, Shandong Province, China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054655700","display_name":"Aijie Cheng","orcid":"https://orcid.org/0000-0001-8547-3189"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Aijie Cheng","raw_affiliation_strings":["School of Mathematics, Shandong University, Jinan 250100, Shandong Province, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Shandong University, Jinan 250100, Shandong Province, China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033227324","display_name":"Hai Xiang Lin","orcid":"https://orcid.org/0000-0002-1653-4854"},"institutions":[{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Hai Xiang Lin","raw_affiliation_strings":["Delft Institute of Applied Mathematics, Delft University of Technology, Delft 2628 CD, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Delft Institute of Applied Mathematics, Delft University of Technology, Delft 2628 CD, The Netherlands","institution_ids":["https://openalex.org/I98358874"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001849550","display_name":"Jan H. van Schuppen","orcid":"https://orcid.org/0000-0001-7150-7915"},"institutions":[{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Jan H. van Schuppen","raw_affiliation_strings":["Delft Institute of Applied Mathematics, Delft University of Technology, Delft 2628 CD, The Netherlands"],"raw_orcid":"https://orcid.org/0000-0001-7150-7915","affiliations":[{"raw_affiliation_string":"Delft Institute of Applied Mathematics, Delft University of Technology, Delft 2628 CD, The Netherlands","institution_ids":["https://openalex.org/I98358874"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100641479","display_name":"Chenghui Zhang","orcid":"https://orcid.org/0000-0003-2317-5930"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chenghui Zhang","raw_affiliation_strings":["School of Control Science and Engineering, Shandong University, Jinan 250061, Shandong Province, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Control Science and Engineering, Shandong University, Jinan 250061, Shandong Province, China","institution_ids":["https://openalex.org/I154099455"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.569,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.66805022,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"22","issue":"2","first_page":"1030","last_page":"1052"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9998999834060669,"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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9991999864578247,"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/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9839000105857849,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/synchronization-networks","display_name":"Synchronization networks","score":0.6582427024841309},{"id":"https://openalex.org/keywords/synchronization","display_name":"Synchronization (alternating current)","score":0.6344550848007202},{"id":"https://openalex.org/keywords/phase-space","display_name":"Phase space","score":0.5947802066802979},{"id":"https://openalex.org/keywords/coupling-strength","display_name":"Coupling strength","score":0.5395407676696777},{"id":"https://openalex.org/keywords/coupling","display_name":"Coupling (piping)","score":0.4890218675136566},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.48473283648490906},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4737551808357239},{"id":"https://openalex.org/keywords/lag","display_name":"Lag","score":0.46622350811958313},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45913463830947876},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.4573298394680023},{"id":"https://openalex.org/keywords/parameter-space","display_name":"Parameter space","score":0.4396902620792389},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.43597376346588135},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.41636553406715393},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3667013645172119},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3491499423980713},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28468650579452515},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.0828147828578949},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07608425617218018},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.06385496258735657}],"concepts":[{"id":"https://openalex.org/C111097370","wikidata":"https://www.wikidata.org/wiki/Q10969923","display_name":"Synchronization networks","level":4,"score":0.6582427024841309},{"id":"https://openalex.org/C2778562939","wikidata":"https://www.wikidata.org/wiki/Q1298791","display_name":"Synchronization (alternating current)","level":3,"score":0.6344550848007202},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.5947802066802979},{"id":"https://openalex.org/C2986219828","wikidata":"https://www.wikidata.org/wiki/Q1193095","display_name":"Coupling strength","level":2,"score":0.5395407676696777},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.4890218675136566},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.48473283648490906},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4737551808357239},{"id":"https://openalex.org/C75778745","wikidata":"https://www.wikidata.org/wiki/Q342626","display_name":"Lag","level":2,"score":0.46622350811958313},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45913463830947876},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.4573298394680023},{"id":"https://openalex.org/C73586568","wikidata":"https://www.wikidata.org/wiki/Q2600211","display_name":"Parameter space","level":2,"score":0.4396902620792389},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.43597376346588135},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.41636553406715393},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3667013645172119},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3491499423980713},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28468650579452515},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0828147828578949},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07608425617218018},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.06385496258735657},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/22m1489502","is_oa":true,"landing_page_url":"https://doi.org/10.1137/22m1489502","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},{"id":"pmh:oai:tudelft.nl:uuid:4974ab34-8a3a-437e-9881-4c8726c119c5","is_oa":true,"landing_page_url":"http://resolver.tudelft.nl/uuid:4974ab34-8a3a-437e-9881-4c8726c119c5","pdf_url":"http://resolver.tudelft.nl/uuid:4974ab34-8a3a-437e-9881-4c8726c119c5","source":{"id":"https://openalex.org/S4306400906","display_name":"Research Repository (Delft University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I98358874","host_organization_name":"Delft University of Technology","host_organization_lineage":["https://openalex.org/I98358874"],"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":"","raw_type":"journal article"}],"best_oa_location":{"id":"doi:10.1137/22m1489502","is_oa":true,"landing_page_url":"https://doi.org/10.1137/22m1489502","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3407508599","display_name":null,"funder_award_id":"ZR2020QF118","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"},{"id":"https://openalex.org/G5631234473","display_name":null,"funder_award_id":"62103235","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6120576256","display_name":null,"funder_award_id":"61821004","funder_id":"https://openalex.org/F4320327720","funder_display_name":"Foundation for Innovative Research Groups of the National Natural Science Foundation of China"},{"id":"https://openalex.org/G878655878","display_name":null,"funder_award_id":"61821004","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/F4320327720","display_name":"Foundation for Innovative Research Groups of the National Natural Science Foundation of China","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1512593738","https://openalex.org/W1965640670","https://openalex.org/W1981733789","https://openalex.org/W1995134411","https://openalex.org/W2015084265","https://openalex.org/W2019861006","https://openalex.org/W2027562147","https://openalex.org/W2033770904","https://openalex.org/W2043883312","https://openalex.org/W2058636918","https://openalex.org/W2103759346","https://openalex.org/W2145137020","https://openalex.org/W2158443610","https://openalex.org/W2262880348","https://openalex.org/W2287982111","https://openalex.org/W2521630792","https://openalex.org/W2528193970","https://openalex.org/W2592776143","https://openalex.org/W2765560143","https://openalex.org/W2906086990","https://openalex.org/W2946038967","https://openalex.org/W2963748836","https://openalex.org/W2963784516","https://openalex.org/W2990566680","https://openalex.org/W3100749211","https://openalex.org/W3102654474","https://openalex.org/W3105447391","https://openalex.org/W4229911014","https://openalex.org/W4232896595","https://openalex.org/W4248666415","https://openalex.org/W4250831670","https://openalex.org/W4386468260"],"related_works":["https://openalex.org/W1537451415","https://openalex.org/W2011726050","https://openalex.org/W1525395558","https://openalex.org/W2241519294","https://openalex.org/W2102366648","https://openalex.org/W2095454919","https://openalex.org/W3104014854","https://openalex.org/W1967359829","https://openalex.org/W1984495201","https://openalex.org/W3125812129"],"abstract_inverted_index":{"&lt;p&gt;The":[0],"synchronization":[1],"stability":[2],"of":[3,8,26,38,64,69,77,87,90,101,107,129],"a":[4,22,94,121,130],"complex":[5],"network":[6,17],"system":[7,25,92],"coupled":[9,28],"phase":[10,29,39,71,159],"oscillators":[11,30],"is":[12,18,61,81,114,117],"discussed.":[13],"In":[14,155],"case":[15],"the":[16,27,36,42,45,50,62,65,70,75,78,84,88,91,102,105,112,126,133,136,149,152,158,162,172],"affected":[19,173],"by":[20,168],"disturbances,":[21],"stochastic":[23],"linearized":[24],"may":[31,54],"be":[32],"used":[33],"to":[34,48,56],"determine":[35],"fluctuations":[37,113,134,150,174],"differences":[40,72,160],"in":[41,96,135,138,151],"lines":[43,52,137],"between":[44],"nodes":[46],"and":[47],"identify":[49],"vulnerable":[51],"that":[53,83,119],"lead":[55],"desynchronization.":[57],"The":[58],"main":[59],"result":[60],"derivation":[63],"asymptotic":[66],"variance":[67],"matrices":[68],"which":[73],"characterizes":[74],"severity":[76],"fluctuations.":[79],"It":[80,116],"found":[82],"cycle":[85,103,140],"space":[86],"graph":[89],"plays":[93],"role":[95],"this":[97,142],"characterization.":[98],"With":[99],"theory":[100],"space,":[104],"effect":[106],"forming":[108],"small":[109],"cycles":[110],"on":[111],"evaluated.":[115],"proven":[118],"adding":[120],"new":[122],"line":[123,131],"or":[124],"increasing":[125],"coupling":[127],"strength":[128],"affects":[132],"any":[139],"including":[141],"line,":[143],"while":[144],"it":[145],"does":[146],"not":[147,166],"affect":[148],"other":[153],"lines.":[154],"particular,":[156],"if":[157],"at":[161],"synchronous":[163],"state":[164],"are":[165],"changed":[167],"these":[169],"actions,":[170],"then":[171],"reduce.&lt;/p&gt;":[175]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
