Discretization of Continuous Dynamical Systems Using UPPAAL

We want to enable the analysis of continuous dynamical systems (where the evolution of a vector of continuous state variables is described by differential equations) by model checking. We do this by showing how such a dynamical system can be translated into a discrete model of communicating timed automata that can be analyzed by the UPPAAL tool. The basis of the translation is the well-known Euler approach for solving differential equations where we use fixed discrete value steps instead of fixed time steps. Each state variable is represented by a timed automaton in which the delay for taking the next value is calculated on the fly using the differential equations. The state variable automata proceed independently but may notify each other when a value step has been completed; this leads to a recalculation of delays. The approach has been implemented in the tool ANIMO for analyzing biological kinase networks in cells. This tool has been used in actual biological research on osteoarthritis dealing with systems where the dimension of the state vector (the number of nodes in the network) is in the order of one hundred.