Summary
Mixed-mode oscillations (MMOs) are characterised by a pattern of small-amplitude oscillations (SAOs) and large-amplitude oscillations (LAOs). They typically occur in systems with multiple time scales, for which intersections between slow manifolds are known to organise the number of SAOs. We investigate the mechanism underlying their generation in the four-dimensional Olsen model for peroxidase-oxidase reaction. In this four-dimensional phase space, we find that the SAOs come about due to the geometry of a surface of heteroclinic connections between two saddle slow manifolds. We employ an advanced numerical set-up to compute the surface of heteroclinic connections through a region of phase space that exhibits a slow passage through a Hopf bifurcation, where the SAOs are generated. Moreover, we compute its intersection curves with two well-chosen hyperplanes. In this way, we show how the surface of heteroclinic connections delimits rotational sectors with given numbers of subsequent SAOs. We also illustrate its role in determining the exit from this region of SAOs and the onset of LAOs.
