Computing All Sparse kinetic Structures for a Lorenz System using Optimization

In this paper, all possible sparse chemical reaction network structures of a classical 3-dimensional Lorenz system are computed assuming a given chemical complex set. The original non-kinetic equations are transformed into kinetic form using two different approaches: firstly, using a statedependent time-rescaling and secondly, by applying the theory of X-factorable systems. Using the notions of core reactions and core complexes, an effective optimization-based computation approach is proposed for the calculation of all structurally different sparse reaction graphs. The resulting structures are briefly analyzed and compared from a structural point of view.