ERODE

ERODE: evaluation and reduction of ordinary differential equations. ERODE is a software tool for the solution and exact reduction of systems of ordinary differential equations (ODEs). The tool supports two recently introduced, complementary, equivalence relations over ODE variables: forward differential equivalence partitions ODE variables into blocks for which a self-consistent aggregate ODE system can be obtained; each aggregate ODE gives the cumulative dynamics of the sum of the original variables in the respective equivalence class. Backward differential equivalence identifies variables that have identical solutions whenever starting from the same initial conditions. ERODE uses a backend based on the well-known Z3 SMT solver to compute the coarsest equivalence that refines a given initial partition. In the special case of ODEs with polynomial derivatives of degree at most two, covering elementary chemical reaction networks (CRNs) and continuous time Markov chains (CTMCs), it implements a more efficient partition-refinement algorithm.