{"id":{"repo_id":"byu","oai_identifier":"oai:scholarsarchive.byu.edu:etd-1634"},"canonical_url":"https://search.dev.ndltd.org/etd/byu/oai:scholarsarchive.byu.edu:etd-1634","repository":{"repo_id":"byu","name":"Brigham Young University","base_url":"https://scholarsarchive.byu.edu/do/oai/"},"display":{"title":"Hopf Bifurcations and Horseshoes Especially Applied to the Brusselator","abstract":"In this paper we explore bifurcations, in particular the Hopf bifurcation. We study this especially in connection with the Brusselator, which is a model of certain chemical reaction-diffusion systems. After a thorough exploration of what a bifurcation is and what classifications there are, we give graphic representations of an occurring Hopf bifurcation in the Brusselator. When an additional forcing term is added, behavior changes dramatically. 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This includes the introduction of a horseshoe in the time map as well as a strange attractor in the system.","abstract_has_math":false,"creators":["Jones, Steven R."],"institution":"Brigham Young University - Provo","degree_name":"MS","degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T01:28:12Z","subjects":["Hopf bifurcation","horseshoe","Brusselator","Mathematics"],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarsarchive.byu.edu/etd/635","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Jones, Steven R."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2005-05-17T07:00:00Z"]},{"key":"dc:publisher","label":"Institution","values":["Brigham Young University - Provo"]},{"key":"dc:type","label":"Dc Type","values":["Selected Project"]},{"key":"thesis:degree_name","label":"Degree Name","values":["MS"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Hopf bifurcation","horseshoe","Brusselator","Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarsarchive.byu.edu/etd/635","https://scholarsarchive.byu.edu/context/etd/article/1634/viewcontent/ETD_CISOPTR_455.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Physical and Mathematical Sciences; Mathematics"]},{"key":"dc:description.abstract","label":"Abstract","values":["In this paper we explore bifurcations, in particular the Hopf bifurcation. We study this especially in connection with the Brusselator, which is a model of certain chemical reaction-diffusion systems. After a thorough exploration of what a bifurcation is and what classifications there are, we give graphic representations of an occurring Hopf bifurcation in the Brusselator. When an additional forcing term is added, behavior changes dramatically. This includes the introduction of a horseshoe in the time map as well as a strange attractor in the system."]},{"key":"dc:format","label":"Dc Format","values":["application:pdf"]},{"key":"dc:source","label":"Dc Source","values":["Brigham Young University - Provo"]},{"key":"dc:title","label":"Title","values":["Hopf Bifurcations and Horseshoes Especially Applied to the Brusselator"]}]}],"canonical_facts":{"dc:creator":["Jones, Steven R."],"dc:date":["2005-05-17T07:00:00Z"],"dc:description":["Physical and Mathematical Sciences; Mathematics"],"dc:description.abstract":["In this paper we explore bifurcations, in particular the Hopf bifurcation. We study this especially in connection with the Brusselator, which is a model of certain chemical reaction-diffusion systems. After a thorough exploration of what a bifurcation is and what classifications there are, we give graphic representations of an occurring Hopf bifurcation in the Brusselator. When an additional forcing term is added, behavior changes dramatically. This includes the introduction of a horseshoe in the time map as well as a strange attractor in the system."],"dc:format":["application:pdf"],"dc:identifier":["https://scholarsarchive.byu.edu/etd/635","https://scholarsarchive.byu.edu/context/etd/article/1634/viewcontent/ETD_CISOPTR_455.pdf"],"dc:language":["English"],"dc:publisher":["Brigham Young University - Provo"],"dc:source":["Brigham Young University - Provo"],"dc:subject":["Hopf bifurcation","horseshoe","Brusselator","Mathematics"],"dc:title":["Hopf Bifurcations and Horseshoes Especially Applied to the Brusselator"],"dc:type":["Selected Project"],"thesis:degree_name":["MS"]},"updated_at":"2026-07-24T01:28:12Z"}