Mixed-mode oscillations (MMOs) are trajectories of a dynamical system in which there is an alternation between oscillations of distinct large and small amplitudes. MMOs have been observed and studied for over thirty years in chemical, physical, and biological systems. Few attempts have been made thus far to classify different patterns of MMOs, in contrast to the classification of the related ph...

Abstract We present a symbolic algorithmic approach that allows to compute invariant manifolds and corresponding reduced systems for differential equations modeling biological networks which comprise chemical reaction cellular biochemistry, compartmental models pharmacology, epidemiology ecology. Multiple time scales of given network are obtained by scaling, based on tropical geometry. Our redu...