{"id":"https://openalex.org/W2418077877","doi":"https://doi.org/10.1137/15m1033228","title":"Stability of a Class of Coupled Hill's Equations and the Lorentz Oscillator Model","display_name":"Stability of a Class of Coupled Hill's Equations and the Lorentz Oscillator Model","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2418077877","doi":"https://doi.org/10.1137/15m1033228","mag":"2418077877"},"language":"en","primary_location":{"id":"doi:10.1137/15m1033228","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1033228","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/A5103237013","display_name":"Hamed Razavi","orcid":"https://orcid.org/0000-0003-1009-3821"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Hamed Razavi","raw_affiliation_strings":["\u2020University of Michigan"],"affiliations":[{"raw_affiliation_string":"\u2020University of Michigan","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101763473","display_name":"Rohit Gupta","orcid":"https://orcid.org/0000-0002-5334-665X"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rohit Gupta","raw_affiliation_strings":["\u2020University of Michigan"],"affiliations":[{"raw_affiliation_string":"\u2020University of Michigan","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045905223","display_name":"Fred C. Adams","orcid":"https://orcid.org/0000-0002-8167-1767"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fred C. Adams","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5091262409","display_name":"Anthony M. Bloch","orcid":"https://orcid.org/0000-0003-0235-9765"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Anthony M. Bloch","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5103237013"],"corresponding_institution_ids":["https://openalex.org/I27837315"],"apc_list":null,"apc_paid":null,"fwci":0.2257,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.57919694,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"15","issue":"2","first_page":"1104","last_page":"1123"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9987999796867371,"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"}},"topics":[{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9987999796867371,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9977999925613403,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9959999918937683,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/floquet-theory","display_name":"Floquet theory","score":0.7977741956710815},{"id":"https://openalex.org/keywords/monodromy-matrix","display_name":"Monodromy matrix","score":0.7974246740341187},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7011536359786987},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6659021377563477},{"id":"https://openalex.org/keywords/monodromy","display_name":"Monodromy","score":0.6313965320587158},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5076180696487427},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.498638391494751},{"id":"https://openalex.org/keywords/hurwitz-matrix","display_name":"Hurwitz matrix","score":0.49058523774147034},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.46058812737464905},{"id":"https://openalex.org/keywords/lorentz-transformation","display_name":"Lorentz transformation","score":0.4530697166919708},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.44651567935943604},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.4283517897129059},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2974590063095093},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.262446790933609},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.21085196733474731},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.13039630651474},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.10662192106246948},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0875803530216217}],"concepts":[{"id":"https://openalex.org/C55649039","wikidata":"https://www.wikidata.org/wiki/Q902618","display_name":"Floquet theory","level":3,"score":0.7977741956710815},{"id":"https://openalex.org/C2780311589","wikidata":"https://www.wikidata.org/wiki/Q6901559","display_name":"Monodromy matrix","level":3,"score":0.7974246740341187},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7011536359786987},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6659021377563477},{"id":"https://openalex.org/C96403706","wikidata":"https://www.wikidata.org/wiki/Q543956","display_name":"Monodromy","level":2,"score":0.6313965320587158},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5076180696487427},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.498638391494751},{"id":"https://openalex.org/C198931094","wikidata":"https://www.wikidata.org/wiki/Q2610096","display_name":"Hurwitz matrix","level":3,"score":0.49058523774147034},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.46058812737464905},{"id":"https://openalex.org/C5667645","wikidata":"https://www.wikidata.org/wiki/Q217255","display_name":"Lorentz transformation","level":2,"score":0.4530697166919708},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44651567935943604},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.4283517897129059},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2974590063095093},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.262446790933609},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.21085196733474731},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.13039630651474},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10662192106246948},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0875803530216217},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/15m1033228","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1033228","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/G6148979255","display_name":null,"funder_award_id":"DMS1207693","funder_id":"https://openalex.org/F4320332172","funder_display_name":"Directorate for Mathematical and Physical Sciences"},{"id":"https://openalex.org/G7720239397","display_name":null,"funder_award_id":"FA9550-14-1-0040","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"}],"funders":[{"id":"https://openalex.org/F4320332172","display_name":"Directorate for Mathematical and Physical Sciences","ror":"https://ror.org/029b7h395"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W92140719","https://openalex.org/W1975911021","https://openalex.org/W1984755140","https://openalex.org/W2011949543","https://openalex.org/W2035660516","https://openalex.org/W2075917906","https://openalex.org/W2076408300","https://openalex.org/W2077952210","https://openalex.org/W2083791232","https://openalex.org/W2090634581","https://openalex.org/W2108435089","https://openalex.org/W2166385804","https://openalex.org/W2169642391"],"related_works":["https://openalex.org/W2374262814","https://openalex.org/W2412051952","https://openalex.org/W1988319246","https://openalex.org/W4386614296","https://openalex.org/W2956219273","https://openalex.org/W3059234765","https://openalex.org/W3105214509","https://openalex.org/W1974901478","https://openalex.org/W3099920733","https://openalex.org/W4246033221"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"study":[4],"the":[5,33,48,52,65,85,87,101],"stability":[6,88],"of":[7,10,17,32,47,51,90,93,100],"a":[8,29,37,45,91],"class":[9],"coupled":[11,66,94,102],"Hill's":[12,67,103],"equations.":[13],"Different":[14],"possible":[15],"forms":[16],"solutions":[18],"are":[19,55,105],"discussed.":[20],"Assuming":[21],"certain":[22],"odd-even":[23],"symmetries":[24],"and":[25,36,61,71],"using":[26,81],"Floquet":[27],"theory,":[28],"simplified":[30],"form":[31,39],"monodromy":[34,53],"matrix":[35],"closed":[38],"formula":[40,83],"for":[41,84],"its":[42,62,78],"eigenvalues,":[43,86],"as":[44,97],"function":[46],"first":[49],"element":[50],"matrix,":[54],"derived.":[56],"The":[57],"Lorentz":[58],"oscillator":[59],"model":[60],"connection":[63],"to":[64,76],"equations":[68],"is":[69,74],"discussed,":[70],"Lyapunov":[72],"theory":[73],"used":[75],"prove":[77],"stability.":[79],"Finally,":[80],"our":[82],"diagrams":[89],"system":[92],"Mathieu":[95],"equations,":[96,104],"an":[98],"example":[99],"generated.":[106]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}