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We use the Litvinov-Maslov correspondence principle to reduce and hybridizenetworks of biochemical reactions. We apply this method to a cell cycleoscillator model. The reduced and hybridized model can be used as a hybridmodel for the cell cycle. We also propose a practical recipe for detectingquasi-equilibrium QE reactions and quasi-steady state QSS species inbiochemical models with rational rate functions and use this recipe for modelreduction. Interestingly, the QE/QSS invariant manifold of the smooth model andthe reduced dynamics along this manifold can be put into correspondence to thetropical variety of the hybridization and to sliding modes along this variety,respectively

Tropical geometries and dynamics of biochemical networks. Application to hybrid cell cycle models