Oscillating Chemical Reactions
Searching for Periodic Behaviour in the Brusselator and Oregonator Models
H.R. Buit (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Z.J.G. Gromotka – Mentor (TU Delft - Mathematical Physics)
D. den Ouden-van der Horst – Graduation committee member (TU Delft - Numerical Analysis)
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Abstract
This thesis aims to identify the parameter combinations necessary for the Brusselator and Oregonator models to exhibit oscillating behavior. Initially, the Brusselator model is reviewed, reproducing the results from [1]. Using Bendixson’s Criterion and the Poincaré-Bendixson Theorem, the existence of stable limit cycles is proven, and the Hopf-Bifurcation locations are derived analytically. The Brusselator model is then extended from a batch reactor to a Continuous Stirred-Tank Reactor to include the inflow of two components previously considered constant. An extensive eigenvalue investigation in Matlab is conducted to determine the parameter combinations that induce oscillating behavior, with Hopf-Bifurcation locations presented in a three-dimensional plot. Lastly, the Oregonator model is introduced and analysed. The existence of limit cycles is proven using similar methods, and an eigenvalue analysis yields the analytic expressions for the Hopf-Bifurcation locations. Periodic solutions are found in all three models, and the necessary parameter combinations are identified.