### Abstract

Original language | English |
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Title of host publication | ModelEd, TestEd, TrustEd |

Editors | Joost-Pieter Katoen, Rom Langerak, Arend Rensink |

Publisher | Springer |

Pages | 297-315 |

Number of pages | 19 |

ISBN (Print) | 978-3-319-68269-3 |

DOIs | |

Publication status | Published - 27 Sep 2017 |

Externally published | Yes |

### Publication series

Series | Lecture Notes in Computer Science |
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### Fingerprint

### Keywords

- Discretization, Euler method, Model Checking, Timed Automata, Systems Biology

### Cite this

*ModelEd, TestEd, TrustEd*(pp. 297-315). Springer. Lecture Notes in Computer Science https://doi.org/10.1007/978-3-319-68270-9_15

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*ModelEd, TestEd, TrustEd.*Springer, Lecture Notes in Computer Science, pp. 297-315. https://doi.org/10.1007/978-3-319-68270-9_15

**Discretization of Continuous Dynamical Systems Using UPPAAL.** / Schivo, Stefano; Langerak, Rom.

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

TY - CHAP

T1 - Discretization of Continuous Dynamical Systems Using UPPAAL

AU - Schivo, Stefano

AU - Langerak, Rom

PY - 2017/9/27

Y1 - 2017/9/27

N2 - 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.

AB - 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.

KW - Discretization, Euler method, Model Checking, Timed Automata, Systems Biology

U2 - 10.1007/978-3-319-68270-9_15

DO - 10.1007/978-3-319-68270-9_15

M3 - Chapter

SN - 978-3-319-68269-3

T3 - Lecture Notes in Computer Science

SP - 297

EP - 315

BT - ModelEd, TestEd, TrustEd

A2 - Katoen, Joost-Pieter

A2 - Langerak, Rom

A2 - Rensink, Arend

PB - Springer

ER -