2023/11/01 by Engel, Maximilian, Olicón-Méndez, Guillermo · 1 citation
#34C26 #34E13 #34E15 #37N25 #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.2311.00575
In this work we study the Brusselator - a prototypical model for chemical oscillations - under the assumption that the bifurcation parameter is of order O(1/ε) for positive ε≪ 1. The dynamics of this mathematical model exhibits a time scale separation visible via fast and slow regimes along its unique attracting limit cycle. Noticeably this limit cycle accumulates at infinity as ε→ 0, so that in polar coordinates (θ,r), and by doing a further change of variable r↦ r-1, we analyse the dynamics near the line at infinity, corresponding to the set \r=0\. This object becomes a nonhyperbolic invariant manifold for which we use a desingularising rescaling, in order to study the closeby dynamics. Further use of geometric singular perturbation techniques allows us to give a decomposition of the Brusselator limit cycle in terms of four different fully quantified time scales.