Title:
Nonlinear oscillation and control in the BZ chemical reaction.

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dc.contributor.advisor Yi, Yingfei
dc.contributor.author Li, Yongfeng en_US
dc.contributor.committeeMember Chow, Shui-Nee
dc.contributor.committeeMember Dieci, Luca
dc.contributor.committeeMember Verriest, Erik
dc.contributor.committeeMember Weiss, Howie
dc.contributor.department Mathematics en_US
dc.date.accessioned 2009-01-22T15:46:21Z
dc.date.available 2009-01-22T15:46:21Z
dc.date.issued 2008-08-25 en_US
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. en_US
dc.description.degree Ph.D. en_US
dc.identifier.uri http://hdl.handle.net/1853/26565
dc.publisher Georgia Institute of Technology en_US
dc.subject Nonlinear oscillation en_US
dc.subject BZ chemical reaction en_US
dc.subject Geometric singular perturbation en_US
dc.subject Model reference control en_US
dc.subject.lcsh Nonequilibrium thermodynamics
dc.subject.lcsh Singular perturbations (Mathematics)
dc.title Nonlinear oscillation and control in the BZ chemical reaction. en_US
dc.type Text
dc.type.genre Dissertation
dspace.entity.type Publication
local.contributor.corporatename College of Sciences
local.contributor.corporatename School of Mathematics
relation.isOrgUnitOfPublication 85042be6-2d68-4e07-b384-e1f908fae48a
relation.isOrgUnitOfPublication 84e5d930-8c17-4e24-96cc-63f5ab63da69
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