In this thesis, analytical solutions of periodic evolutions of the Brusselator with a harmonic diffusion are obtained through the generalized harmonic balance method. The stability and bifurcation of the periodic evolutions are determined by the eigenvalue analysis. The bifurcation trees of period-1 to period-8 evolutions of the Brusselator are presented by frequency–amplitude characteristics. To illustrate the accuracy of the analytical prediction for periodic evolutions of the Brusselator, numerical simulations of the stable period-m (m=1, 2, 4, 8) evolutions are completed. The harmonic amplitude spectrums are presented to estimate the truncation error of the analytical prediction, and each harmonic contribution on the specific periodic evolution can be achieved. This study gives a better understanding of periodic evolutions to chaos in the slowly varying Brusselator system, and the bifurcation trees of period-1 evolution to chaos are clearly demonstrated, which can help one understand a route of periodic evolution to chaos in chemical reaction oscillators. From this study, the generalized harmonic balance method is a good method for slowly varying systems, and such a method provides very accurate solutions of periodic motions in such nonlinear systems.
|Advisor:||Luo, Albert Chao Jun|
|Commitee:||Chen, Xin, Wang, Fengxia|
|School:||Southern Illinois University at Edwardsville|
|Department:||Mechanical and Industrial Engineering|
|School Location:||United States -- Illinois|
|Source:||MAI 58/01M(E), Masters Abstracts International|
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