Key Words Kinetics Model reduction Grids Invariant manifold Entropy Non-linear

dynamics Mathematical modelling Numerical methods Complexity in the description of big chemical reaction networks has both struc-tural (number of species and reactions) and temporal (very different reaction rates) aspects. A consistent way to make model reduction is to construct the invariant manifold which describes the asymptotic system behaviour. In this pa-per we present a discrete analog of this object: an invariant grid. The invariant grid is introduced independently from the invariant manifold notion and can serve to represent the dynamic system behaviour as well as to approximate the invariant manifold after refi nement. The method is designed for pure dissipative systems and widely uses their thermodynamic properties but allows also gener-alizations for some classes of open systems. The method is illustrated by two examples: the simplest catalytic reaction (Michaelis-Menten mechanism) and the hydrogen oxidation