Slow manifolds and mixed-mode oscillations in the Belousov–Zhabotinskii reaction

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Abstract
The mixed-mode oscillations observed at high flow rates in the Belousov–Zhabotinskii (BZ) reaction are considered and comparison is made between these oscillations and the dynamics of three different mathematical models based on slow manifolds. It is shown that the model proposed by Rössler for the generation of complex behavior in nonequilibrium chemical reactions is in conflict with the behavior of the BZ reaction. It is also shown that a slow-manifold model based on the hysteresis-Hopf normal form fails to accurately reproduce the oscillations found at high flow rates in the BZ system. A model of the type first proposed by Boissonade is presented; the model consists of the coupling of two simple systems. It is shown that this model naturally generates mixed-mode oscillations like those observed in the BZ reaction.