  Piecewise smooth hybrid systems, involving continuous and discrete variables,
are suitable models for describing the multiscale regulatory machinery of the
biological cells. In hybrid models, the discrete variables can switch on and
off some molecular interactions, simulating cell progression through a series
of functioning modes. The advancement through the cell cycle is the archetype
of such an organized sequence of events. We present an approach, inspired from
tropical geometry ideas, allowing to reduce, hybridize and analyse cell cycle
models consisting of polynomial or rational ordinary differential equations.
