Discretization of Continuous Dynamical Systems Using UPPAAL

Chapter
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Part of the Lecture Notes in Computer Science book series (LNCS, volume 10500)

Abstract

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.

Keywords

Discretization Euler method Model checking Timed automata Systems biology 
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Notes

Acknowledgements

We thank Arend Rensink for an important comment on an earlier version of this work. We thank Wim Bos, Liesbeth Geris, Marcel Karperien, Johan Kerkhofs, Jaco van de Pol, Janine Post, Jetse Scholma, Ricardo Urquidi Camacho, Paul van der Vet, and Brend Wanders for the fruitful and pleasant collaboration leading to ANIMO.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Formal Methods and Tools Group, Faculty of EEMCSUniversity of TwenteEnschedeThe Netherlands

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