{"id":"https://openalex.org/W2437001323","doi":"https://doi.org/10.1137/15m1038438","title":"Persistence of Homoclinic Orbits under White Noise Perturbation","display_name":"Persistence of Homoclinic Orbits under White Noise Perturbation","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2437001323","doi":"https://doi.org/10.1137/15m1038438","mag":"2437001323"},"language":"en","primary_location":{"id":"doi:10.1137/15m1038438","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1038438","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/A5101509604","display_name":"Nan Lu","orcid":"https://orcid.org/0000-0002-5867-2411"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Nan Lu","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101509604"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.09418492,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"15","issue":"2","first_page":"1124","last_page":"1142"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9932000041007996,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/homoclinic-orbit","display_name":"Homoclinic orbit","score":0.9682016968727112},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6666949391365051},{"id":"https://openalex.org/keywords/white-noise","display_name":"White noise","score":0.6429342031478882},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.6419799327850342},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.5972089767456055},{"id":"https://openalex.org/keywords/persistence","display_name":"Persistence (discontinuity)","score":0.54157954454422},{"id":"https://openalex.org/keywords/periodic-orbits","display_name":"Periodic orbits","score":0.5369396805763245},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.47463855147361755},{"id":"https://openalex.org/keywords/homoclinic-bifurcation","display_name":"Homoclinic bifurcation","score":0.4623478651046753},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4516907036304474},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.45150813460350037},{"id":"https://openalex.org/keywords/invariant-manifold","display_name":"Invariant manifold","score":0.4492083489894867},{"id":"https://openalex.org/keywords/stable-manifold","display_name":"Stable manifold","score":0.41101759672164917},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3135150074958801},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19273704290390015},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.18112510442733765},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.14616256952285767},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.14395743608474731},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07460957765579224}],"concepts":[{"id":"https://openalex.org/C200581526","wikidata":"https://www.wikidata.org/wiki/Q690494","display_name":"Homoclinic orbit","level":4,"score":0.9682016968727112},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6666949391365051},{"id":"https://openalex.org/C112633086","wikidata":"https://www.wikidata.org/wiki/Q381287","display_name":"White noise","level":2,"score":0.6429342031478882},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.6419799327850342},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5972089767456055},{"id":"https://openalex.org/C2781009140","wikidata":"https://www.wikidata.org/wiki/Q7170389","display_name":"Persistence (discontinuity)","level":2,"score":0.54157954454422},{"id":"https://openalex.org/C2984157986","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Periodic orbits","level":2,"score":0.5369396805763245},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.47463855147361755},{"id":"https://openalex.org/C155405617","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Homoclinic bifurcation","level":5,"score":0.4623478651046753},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4516907036304474},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.45150813460350037},{"id":"https://openalex.org/C20483540","wikidata":"https://www.wikidata.org/wiki/Q4200516","display_name":"Invariant manifold","level":2,"score":0.4492083489894867},{"id":"https://openalex.org/C50429861","wikidata":"https://www.wikidata.org/wiki/Q3554830","display_name":"Stable manifold","level":2,"score":0.41101759672164917},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3135150074958801},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19273704290390015},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.18112510442733765},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.14616256952285767},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.14395743608474731},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07460957765579224},{"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/C187320778","wikidata":"https://www.wikidata.org/wiki/Q1349130","display_name":"Geotechnical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/15m1038438","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1038438","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":[],"awards":[{"id":"https://openalex.org/G8212724206","display_name":null,"funder_award_id":"DMS-1500159","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"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1582770960","https://openalex.org/W1594115232","https://openalex.org/W1963932485","https://openalex.org/W2027447627","https://openalex.org/W2058847436","https://openalex.org/W2060802919","https://openalex.org/W2060849920","https://openalex.org/W2068495549","https://openalex.org/W2074189340","https://openalex.org/W2092680287","https://openalex.org/W2163088626","https://openalex.org/W2963745976","https://openalex.org/W2964213699","https://openalex.org/W3123094903"],"related_works":["https://openalex.org/W1984913125","https://openalex.org/W2955054485","https://openalex.org/W2147240237","https://openalex.org/W2358211602","https://openalex.org/W2353823404","https://openalex.org/W2000817226","https://openalex.org/W2096695703","https://openalex.org/W2018447484","https://openalex.org/W2061154922","https://openalex.org/W1972846926"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"study":[4],"the":[5,38,43],"persistence":[6,44],"of":[7,33,37,45],"homoclinic":[8,46],"orbits":[9,47],"for":[10,48],"some":[11],"second":[12],"order":[13],"ordinary":[14],"differential":[15],"equations":[16],"subject":[17],"to":[18,41],"small":[19],"multiplicative":[20],"white":[21],"noise":[22],"perturbation.":[23],"We":[24],"obtain":[25],"a":[26,35],"path-independent":[27],"criterion,":[28],"which":[29],"can":[30],"be":[31],"thought":[32],"as":[34],"generalization":[36],"Melnikov":[39],"integral,":[40],"ensure":[42],"almost":[49],"all":[50],"sample":[51],"paths.":[52],"The":[53],"proof":[54],"is":[55],"based":[56],"on":[57],"invariant":[58],"manifold":[59],"theory":[60],"and":[61],"Melnikov-type":[62],"analysis.":[63]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}