{"id":{"repo_id":"gatech","oai_identifier":"oai:repository.gatech.edu:1853/26565"},"canonical_url":"https://search.dev.ndltd.org/etd/gatech/oai:repository.gatech.edu:1853/26565","repository":{"repo_id":"gatech","name":"Georgia Tech","base_url":"https://repository.gatech.edu/server/oai/request"},"display":{"title":"Nonlinear oscillation and control in the BZ chemical reaction.","abstract":"In this thesis, a reversible Lotka-Volterra model was proposed to study the nonlinear oscillation of the Belousov-Zhabotinsky(BZ) reaction in a closed isothermal chemical system. The reaction zone can be divided into two zones, oscillation zone and transition zone, where the oscillation time and the transition time and the number of the complete oscillations are estimated. By applying the geometric singular perturbation method, it was proved that there exist an oscillation axis in the oscillation zone, a strongly stable two-dimensional invariant manifold in transition zone, on which there is also a one-dimensional stable invariant manifold, which is the part of the central axis. There is no oscillation in the vicinity of the equilibrium, as indicated by Onsager's reciprocal symmetry relation. Furthermore, the damped oscillation is studied in terms of the action-action-angle variables. In the end, the model reference control technique is employed to control the oscillation amplitude in the BZ reaction.","abstract_html":"In this thesis, a reversible Lotka-Volterra model was proposed to study the nonlinear oscillation of the Belousov-Zhabotinsky(BZ) reaction in a closed isothermal chemical system. The reaction zone can be divided into two zones, oscillation zone and transition zone, where the oscillation time and the transition time and the number of the complete oscillations are estimated. By applying the geometric singular perturbation method, it was proved that there exist an oscillation axis in the oscillation zone, a strongly stable two-dimensional invariant manifold in transition zone, on which there is also a one-dimensional stable invariant manifold, which is the part of the central axis. There is no oscillation in the vicinity of the equilibrium, as indicated by Onsager's reciprocal symmetry relation. Furthermore, the damped oscillation is studied in terms of the action-action-angle variables. In the end, the model reference control technique is employed to control the oscillation amplitude in the BZ reaction.","abstract_has_math":false,"creators":["Li, Yongfeng"],"institution":"Georgia Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Mathematics","school":null,"contributors":[],"advisors":["Yi, Yingfei"],"committee_chairs":[],"committee_members":["Chow, Shui-Nee","Dieci, Luca","Verriest, Erik","Weiss, Howie"],"year":2008,"date_issued":"2008-08-25","date_published":"2008-08-25","updated_at":"2026-07-27T19:50:47Z","subjects":["Nonlinear oscillation","BZ chemical reaction","Geometric singular perturbation","Model reference control"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/1853/26565","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Yi, Yingfei"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Chow, Shui-Nee","Dieci, Luca","Verriest, Erik","Weiss, Howie"]},{"key":"dc:contributor.department","label":"Department","values":["Mathematics"]},{"key":"dc:creator","label":"Author","values":["Li, Yongfeng"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2009-01-22T15:46:21Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2009-01-22T15:46:21Z"]},{"key":"dc:date.issued","label":"Date","values":["2008-08-25"]},{"key":"dc:publisher","label":"Institution","values":["Georgia Institute of Technology"]},{"key":"dc:type","label":"Dc Type","values":["Text"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Nonlinear oscillation","BZ chemical reaction","Geometric singular perturbation","Model reference control"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1853/26565"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis, a reversible Lotka-Volterra model was proposed to study the nonlinear oscillation of the Belousov-Zhabotinsky(BZ) reaction in a closed isothermal chemical system. The reaction zone can be divided into two zones, oscillation zone and transition zone, where the oscillation time and the transition time and the number of the complete oscillations are estimated. By applying the geometric singular perturbation method, it was proved that there exist an oscillation axis in the oscillation zone, a strongly stable two-dimensional invariant manifold in transition zone, on which there is also a one-dimensional stable invariant manifold, which is the part of the central axis. There is no oscillation in the vicinity of the equilibrium, as indicated by Onsager's reciprocal symmetry relation. Furthermore, the damped oscillation is studied in terms of the action-action-angle variables. In the end, the model reference control technique is employed to control the oscillation amplitude in the BZ reaction."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph.D."]},{"key":"dc:title","label":"Title","values":["Nonlinear oscillation and control in the BZ chemical reaction."]}]}],"canonical_facts":{"dc:contributor.advisor":["Yi, Yingfei"],"dc:contributor.committeemember":["Chow, Shui-Nee","Dieci, Luca","Verriest, Erik","Weiss, Howie"],"dc:contributor.department":["Mathematics"],"dc:creator":["Li, Yongfeng"],"dc:date.accessioned":["2009-01-22T15:46:21Z"],"dc:date.available":["2009-01-22T15:46:21Z"],"dc:date.issued":["2008-08-25"],"dc:description.abstract":["In this thesis, a reversible Lotka-Volterra model was proposed to study the nonlinear oscillation of the Belousov-Zhabotinsky(BZ) reaction in a closed isothermal chemical system. The reaction zone can be divided into two zones, oscillation zone and transition zone, where the oscillation time and the transition time and the number of the complete oscillations are estimated. By applying the geometric singular perturbation method, it was proved that there exist an oscillation axis in the oscillation zone, a strongly stable two-dimensional invariant manifold in transition zone, on which there is also a one-dimensional stable invariant manifold, which is the part of the central axis. There is no oscillation in the vicinity of the equilibrium, as indicated by Onsager's reciprocal symmetry relation. Furthermore, the damped oscillation is studied in terms of the action-action-angle variables. In the end, the model reference control technique is employed to control the oscillation amplitude in the BZ reaction."],"dc:description.degree":["Ph.D."],"dc:identifier.uri":["http://hdl.handle.net/1853/26565"],"dc:publisher":["Georgia Institute of Technology"],"dc:subject":["Nonlinear oscillation","BZ chemical reaction","Geometric singular perturbation","Model reference control"],"dc:title":["Nonlinear oscillation and control in the BZ chemical reaction."],"dc:type":["Text"]},"updated_at":"2026-07-27T19:50:47Z"}