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Pattern formation in the Brusselator model of chemical reactions
Dissertation (MSc)--University of Pretoria, 2016.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2016
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| _version_ | 1867613544305917952 |
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| access_status_str | Open Access |
| author2 | Anguelov, Roumen |
| author_browse | Anguelov, Roumen |
| author_facet | Anguelov, Roumen |
| collection | Thesis |
| dc_rights_str_mv | © 2016 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. |
| description | Dissertation (MSc)--University of Pretoria, 2016. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/57289 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:37:50.174Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2016 |
| publishDateRange | 2016 |
| publishDateSort | 2016 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/57289 Pattern formation in the Brusselator model of chemical reactions Anguelov, Roumen smstoltz@live.co.za Stoltz, Stephanus Marnus UCTD Dissertation (MSc)--University of Pretoria, 2016. The Brusselator model is widely used to illustrate and study basic features of models of chemical reactions involving trimolecular steps. We provide the necessary mathematical theory related to Reaction-Diffusion systems in general and to the Brusselator model in particular. Specifically, the issues of local and global existence of solutions, their uniqueness and regularity are discussed in detail. The theoretical and numerical investigation presented futher in the thesis provides an insight into the asymptotic behavior of the solutions of this model, characterizing the parameter region for each of the three qualitatively different cases: homogeneous steady state, Turing pattern and bulk oscillations. Particular attention is given to the supercritical Hopf bifurcation parameter domain where no substantial theory is available. This study was largely motivated by the observations of Young, Zhabotinsky and Epstein that Turing patterns eventually (for sufficiently small ratio of the diffusion coefficients) dominate the Hopf bifurcation induced bulk oscillations. In this work we confirm this observation and further establish more precisely the shape of the boundary separating the Turing pattern domain and the bulk oscillations domain in the parameter space. The obtained results are used in revealing an essential mechanism generating oscillating patterns in the coupled Brusselator model. It can be considered as a model of the reaction sequences in two thin layers of gel that meet at an interface. Each layer contains the same reactants with the same kinetics but with different diffusion coefficients. The occurrence of oscillating patterns is due to the fact that for the same values of the parameters of the model but with different diffusion coefficients the one system can be in the Turing pattern domain while the other is in the bulk oscillations domain. Hence, roughly speaking, one layer provides a pattern while the other layer drives the oscillations. tm2016 Mathematics and Applied Mathematics MSc Unrestricted 2016-10-14T07:33:06Z 2016-10-14T07:33:06Z 2016-09-01 2016 Dissertation Stoltz, SM 2016, Pattern formation in the Brusselator model of chemical reactions, MSc Dissertation, University of Pretoria, Pretoria, viewed yymmdd <http://hdl.handle.net/2263/57289> S2016 http://hdl.handle.net/2263/57289 en © 2016 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. application/pdf University of Pretoria |
| spellingShingle | UCTD Pattern formation in the Brusselator model of chemical reactions |
| title | Pattern formation in the Brusselator model of chemical reactions |
| title_full | Pattern formation in the Brusselator model of chemical reactions |
| title_fullStr | Pattern formation in the Brusselator model of chemical reactions |
| title_full_unstemmed | Pattern formation in the Brusselator model of chemical reactions |
| title_short | Pattern formation in the Brusselator model of chemical reactions |
| title_sort | pattern formation in the brusselator model of chemical reactions |
| topic | UCTD |
| url | http://hdl.handle.net/2263/57289 |