{"id":"https://openalex.org/W3206902949","doi":"https://doi.org/10.1137/20m1364345","title":"Singularities of Invariant Densities for Random Switching between Two Linear ODEs in 2D","display_name":"Singularities of Invariant Densities for Random Switching between Two Linear ODEs in 2D","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3206902949","doi":"https://doi.org/10.1137/20m1364345","mag":"3206902949"},"language":"en","primary_location":{"id":"doi:10.1137/20m1364345","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1364345","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":null,"license_id":null,"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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061445771","display_name":"Yuri Bakhtin","orcid":"https://orcid.org/0000-0003-1125-4543"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yuri Bakhtin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003566326","display_name":"Tobias Hurth","orcid":"https://orcid.org/0000-0002-1093-091X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tobias Hurth","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001461789","display_name":"Sean D. Lawley","orcid":"https://orcid.org/0000-0003-2208-026X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sean D. Lawley","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-2208-026X","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5000362971","display_name":"Jonathan C. Mattingly","orcid":"https://orcid.org/0000-0002-1819-729X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jonathan C. Mattingly","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8681,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.71321599,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"20","issue":"4","first_page":"1917","last_page":"1958"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9804999828338623,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9804999828338623,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13187","display_name":"Diffusion and Search Dynamics","score":0.9193999767303467,"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/gravitational-singularity","display_name":"Gravitational singularity","score":0.8530749082565308},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.8175933957099915},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6750388741493225},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5013315677642822},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34415149688720703},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2863529920578003},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.0983937680721283}],"concepts":[{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.8530749082565308},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.8175933957099915},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6750388741493225},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5013315677642822},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34415149688720703},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2863529920578003},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0983937680721283}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/20m1364345","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1364345","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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","display_name":"Quality Education","score":0.5}],"awards":[{"id":"https://openalex.org/G1262627033","display_name":"Ergodic Theory of Complex Random Dynamics","funder_award_id":"1460595","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G1478422232","display_name":"Collaborative Research: Propagation of Dissipation: Stochastic Stabilization in Finite and Infinite Dimensions","funder_award_id":"1613337","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G1748676385","display_name":null,"funder_award_id":"DMS-1613337","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G2993528629","display_name":null,"funder_award_id":"200021 - 175728/1","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G3503556581","display_name":"CAREER: How Diffusion, Dimension, Geometry, and Redundancy Affect Cellular Dynamics","funder_award_id":"1944574","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3561874305","display_name":"Ergodic Properties of Piecewise Deterministic Markov Processes, Stochastic Peristence and Algorithmic Aspects of Self Interacting Processes","funder_award_id":"175728","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G4408519005","display_name":null,"funder_award_id":"DMS-1460595","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G4483326994","display_name":null,"funder_award_id":"DMS-1811444","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G6985892910","display_name":"Asymptotic Problems in Random Dynamics","funder_award_id":"1811444","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8426347965","display_name":null,"funder_award_id":"DMS-1944574","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G8445800797","display_name":null,"funder_award_id":"DMS-1814832","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G8978424680","display_name":"Diffusion in Stochastic Environments: Analysis and Biological Applications","funder_award_id":"1814832","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G993971353","display_name":null,"funder_award_id":"200021","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1885308736","https://openalex.org/W1906471536","https://openalex.org/W1971765957","https://openalex.org/W2092922447","https://openalex.org/W2108566619","https://openalex.org/W2109826688","https://openalex.org/W2111167674","https://openalex.org/W2122121413","https://openalex.org/W2125132416","https://openalex.org/W2168804240","https://openalex.org/W2277080394","https://openalex.org/W2585592087","https://openalex.org/W2606478833","https://openalex.org/W2743730707","https://openalex.org/W2746595772","https://openalex.org/W2794653150","https://openalex.org/W2963497144","https://openalex.org/W3100992554","https://openalex.org/W3103472687","https://openalex.org/W3103901317","https://openalex.org/W3104122450","https://openalex.org/W3106364061"],"related_works":["https://openalex.org/W2371448224","https://openalex.org/W3134495997","https://openalex.org/W2363680170","https://openalex.org/W2376428685","https://openalex.org/W4256082577","https://openalex.org/W625783435","https://openalex.org/W2048742619","https://openalex.org/W2384641672","https://openalex.org/W2742179975","https://openalex.org/W2032519770"],"abstract_inverted_index":{"We":[0,22,38,45],"consider":[1],"a":[2],"planar":[3],"dynamical":[4],"system":[5],"generated":[6],"by":[7],"two":[8],"stable":[9],"linear":[10],"vector":[11],"fields":[12],"with":[13],"distinct":[14],"fixed":[15],"points":[16],"and":[17,35],"random":[18],"switching":[19,33],"between":[20],"them.":[21],"characterize":[23],"singularities":[24],"of":[25,31],"the":[26,32],"invariant":[27],"density":[28],"in":[29],"terms":[30],"rates":[34],"contraction":[36],"rates.":[37],"prove":[39],"boundedness":[40],"away":[41],"from":[42],"those":[43],"singularities.":[44],"also":[46],"discuss":[47],"some":[48],"motivating":[49],"biological":[50],"examples.":[51]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-08-22T07:34:49.880490","created_date":"2025-10-10T00:00:00"}