{"id":"https://openalex.org/W2018258573","doi":"https://doi.org/10.1137/080731360","title":"Analysis of a Stochastic Chemical System Close to a SNIPER Bifurcation of Its Mean-Field Model","display_name":"Analysis of a Stochastic Chemical System Close to a SNIPER Bifurcation of Its Mean-Field Model","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2018258573","doi":"https://doi.org/10.1137/080731360","mag":"2018258573"},"language":"en","primary_location":{"id":"doi:10.1137/080731360","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080731360","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied Mathematics","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/A5085919327","display_name":"Radek Erban","orcid":"https://orcid.org/0000-0001-8470-3763"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]},{"id":"https://openalex.org/I4210120676","display_name":"Mathematical Institute of the Slovak Academy of Sciences","ror":"https://ror.org/02fhy7464","country_code":"SK","type":"facility","lineage":["https://openalex.org/I207624831","https://openalex.org/I4210120676"]}],"countries":["GB","SK"],"is_corresponding":false,"raw_author_name":"Radek Erban","raw_affiliation_strings":["Mathematical Institute, University of Oxford, 24-29 St. Giles', Oxford, OX1 3LB, United King"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Oxford, 24-29 St. Giles', Oxford, OX1 3LB, United King","institution_ids":["https://openalex.org/I4210120676","https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081545907","display_name":"S. Jonathan Chapman","orcid":"https://orcid.org/0000-0003-3347-6024"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]},{"id":"https://openalex.org/I4210120676","display_name":"Mathematical Institute of the Slovak Academy of Sciences","ror":"https://ror.org/02fhy7464","country_code":"SK","type":"facility","lineage":["https://openalex.org/I207624831","https://openalex.org/I4210120676"]}],"countries":["GB","SK"],"is_corresponding":false,"raw_author_name":"S. Jonathan Chapman","raw_affiliation_strings":["Mathematical Institute, University of Oxford, 24-29 St. Giles', Oxford, OX1 3LB, United King"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Oxford, 24-29 St. Giles', Oxford, OX1 3LB, United King","institution_ids":["https://openalex.org/I4210120676","https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036566464","display_name":"Ioannis G. Kevrekidis","orcid":"https://orcid.org/0000-0003-2220-3522"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ioannis G. Kevrekidis","raw_affiliation_strings":["Department of Chemical Engineering, PACM, and Mathematics, Princeton University, Engineer-ing Quadrangle, Olden Street, Princeton, NJ 08544"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Chemical Engineering, PACM, and Mathematics, Princeton University, Engineer-ing Quadrangle, Olden Street, Princeton, NJ 08544","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055213689","display_name":"Tom\u00e1\u0161 Vejchodsk\u00fd","orcid":"https://orcid.org/0000-0002-3054-5306"},"institutions":[{"id":"https://openalex.org/I2801315873","display_name":"Somerville Hospital","ror":"https://ror.org/023pf5e38","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I124574311","https://openalex.org/I2801315873"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tom\u00e1\u0161 Vejchodsk\u00fd","raw_affiliation_strings":["Oxford; Linacre College, Oxford;","Somerville College, Oxford;","\u017ditn\u00e1 25, 115 67 Praha 1, Czech Republic"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Oxford; Linacre College, Oxford;","institution_ids":[]},{"raw_affiliation_string":"Somerville College, Oxford;","institution_ids":["https://openalex.org/I2801315873"]},{"raw_affiliation_string":"\u017ditn\u00e1 25, 115 67 Praha 1, Czech Republic","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9585,"has_fulltext":false,"cited_by_count":52,"citation_normalized_percentile":{"value":0.74006803,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"70","issue":"3","first_page":"984","last_page":"1016"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9951000213623047,"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"}},{"id":"https://openalex.org/T13539","display_name":"thermodynamics and calorimetric analyses","score":0.989799976348877,"subfield":{"id":"https://openalex.org/subfields/1606","display_name":"Physical and Theoretical Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/fokker\u2013planck-equation","display_name":"Fokker\u2013Planck equation","score":0.6730905175209045},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5727764368057251},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5455313920974731},{"id":"https://openalex.org/keywords/oscillation","display_name":"Oscillation (cell signaling)","score":0.5383331179618835},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5330575704574585},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.4318448305130005},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.42755448818206787},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3842783570289612},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35434579849243164},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3412514328956604},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.22728118300437927},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1275063455104828},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.11764124035835266},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.10621678829193115}],"concepts":[{"id":"https://openalex.org/C69123182","wikidata":"https://www.wikidata.org/wiki/Q891766","display_name":"Fokker\u2013Planck equation","level":3,"score":0.6730905175209045},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5727764368057251},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5455313920974731},{"id":"https://openalex.org/C2778439541","wikidata":"https://www.wikidata.org/wiki/Q7106412","display_name":"Oscillation (cell signaling)","level":2,"score":0.5383331179618835},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5330575704574585},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.4318448305130005},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.42755448818206787},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3842783570289612},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35434579849243164},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3412514328956604},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.22728118300437927},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1275063455104828},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.11764124035835266},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.10621678829193115},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/080731360","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080731360","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:uuid:6715aa33-48ea-4173-836d-f911b097bc13","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"http://eprints.maths.ox.ac.uk/837","raw_type":"Article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.155.3575","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.155.3575","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.cas.cz/~vejchod/73136.pdf","raw_type":"text"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:6715aa33-48ea-4173-836d-f911b097bc13","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:6715aa33-48ea-4173-836d-f911b097bc13","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://eprints.maths.ox.ac.uk/837","raw_type":"Journal article"},{"id":"pmh:oai:repository.kaust.edu.sa:10754/597550","is_oa":false,"landing_page_url":"http://hdl.handle.net/10754/597550","pdf_url":null,"source":{"id":"https://openalex.org/S4306401596","display_name":"King Abdullah University of Science and Technology Repository (King Abdullah University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I71920554","host_organization_name":"King Abdullah University of Science and Technology","host_organization_lineage":["https://openalex.org/I71920554"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2738863136","display_name":null,"funder_award_id":"IAA100760702","funder_id":"https://openalex.org/F4320322482","funder_display_name":"Akademie V\u011bd \u010cesk\u00e9 Republiky"},{"id":"https://openalex.org/G480621758","display_name":null,"funder_award_id":"AV0Z10190503","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"},{"id":"https://openalex.org/G6732639758","display_name":null,"funder_award_id":"AV0Z10190503","funder_id":"https://openalex.org/F4320322482","funder_display_name":"Akademie V\u011bd \u010cesk\u00e9 Republiky"},{"id":"https://openalex.org/G7255873218","display_name":null,"funder_award_id":"KUK-C1-013-04","funder_id":"https://openalex.org/F4320322320","funder_display_name":"King Abdullah University of Science and Technology"},{"id":"https://openalex.org/G8673896826","display_name":null,"funder_award_id":"KUK-C1-013-04","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320321006","display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","ror":"https://ror.org/01pv73b02"},{"id":"https://openalex.org/F4320322320","display_name":"King Abdullah University of Science and Technology","ror":"https://ror.org/01q3tbs38"},{"id":"https://openalex.org/F4320322482","display_name":"Akademie V\u011bd \u010cesk\u00e9 Republiky","ror":"https://ror.org/053avzc18"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1638774395","https://openalex.org/W1968316870","https://openalex.org/W1989843376","https://openalex.org/W2017277760","https://openalex.org/W2022884290","https://openalex.org/W2025830947","https://openalex.org/W2046451925","https://openalex.org/W2065949669","https://openalex.org/W2084924279","https://openalex.org/W2094782094","https://openalex.org/W2114849571","https://openalex.org/W2155418451","https://openalex.org/W2164761951","https://openalex.org/W3021559346","https://openalex.org/W3098041616","https://openalex.org/W4230906466"],"related_works":["https://openalex.org/W4225624922","https://openalex.org/W3215350949","https://openalex.org/W1977915423","https://openalex.org/W2962853738","https://openalex.org/W1995547106","https://openalex.org/W1989512732","https://openalex.org/W1967504243","https://openalex.org/W2120537744","https://openalex.org/W2114785653","https://openalex.org/W2046214901"],"abstract_inverted_index":{"A":[0],"framework":[1],"for":[2,11,31,50,53,155],"the":[3,13,34,43,55,64,71,74,80,83,96,105,110,122,135,146,156,164,172],"analysis":[4,144],"of":[5,8,36,63,67,73,82,86,109,145,158,163,171],"stochastic":[6,44],"models":[7],"chemical":[9,97,115,123],"systems":[10],"which":[12,54],"deterministic":[14],"mean-field":[15,56],"description":[16],"is":[17,25,40,93,117,126,149],"undergoing":[18],"a":[19,28,112,161,169],"saddle-node":[20],"infinite":[21],"period":[22,66,157],"(SNIPER)":[23],"bifurcation":[24,29],"presented.":[26,140],"Such":[27],"occurs,":[30],"example,":[32],"in":[33,128],"modeling":[35],"cell-cycle":[37],"regulation.":[38],"It":[39],"shown":[41],"that":[42],"system":[45,84,173],"possesses":[46],"oscillatory":[47],"solutions":[48],"even":[49],"parameter":[51],"values":[52],"model":[57,75],"does":[58],"not":[59],"oscillate.":[60],"The":[61],"dependence":[62],"mean":[65],"these":[68],"oscillations":[69],"on":[70,95],"parameters":[72],"(kinetic":[76],"rate":[77,165],"constants)":[78],"and":[79,107,120,167],"size":[81],"(number":[85],"molecules":[87],"present)":[88],"are":[89,139],"studied.":[90],"Our":[91],"approach":[92],"based":[94],"Fokker\u2013Planck":[98,136,147],"equation.":[99],"To":[100],"gain":[101],"some":[102],"insight":[103],"into":[104],"advantages":[106],"disadvantages":[108],"method,":[111],"simple":[113],"one-dimensional":[114],"switch":[116],"first":[118],"analyzed,":[119],"then":[121],"SNIPER":[124],"problem":[125],"studied":[127],"detail.":[129],"First,":[130],"results":[131],"obtained":[132],"by":[133],"solving":[134],"equation":[137,148],"numerically":[138],"Then":[141],"an":[142],"asymptotic":[143],"used":[150],"to":[151],"derive":[152],"explicit":[153],"formulae":[154],"oscillation":[159],"as":[160,168],"function":[162,170],"constants":[166],"size.":[174]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":4}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
