### Abstract

Original language | English |
---|---|

Title of host publication | ModelEd, TestEd, TrustEd |

Subtitle of host publication | Essays Dedicated to Ed Brinksma on the Occasion of His 60th Birthday |

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

Publisher | Springer |

Pages | 297-315 |

Number of pages | 19 |

ISBN (Electronic) | 978-3-319-68270-9 |

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

DOIs | |

State | Published - 27 Sep 2017 |

### Publication series

Name | Lecture Notes in Computer Science |
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Publisher | Springer |

Volume | 10500 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Fingerprint

### Keywords

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

### Cite this

*ModelEd, TestEd, TrustEd: Essays Dedicated to Ed Brinksma on the Occasion of His 60th Birthday*(pp. 297-315). (Lecture Notes in Computer Science; Vol. 10500). Springer. DOI: 10.1007/978-3-319-68270-9_15

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*ModelEd, TestEd, TrustEd: Essays Dedicated to Ed Brinksma on the Occasion of His 60th Birthday.*Lecture Notes in Computer Science, vol. 10500, Springer, pp. 297-315. DOI: 10.1007/978-3-319-68270-9_15

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

Research output: Scientific - peer-review › Chapter

TY - CHAP

T1 - Discretization of Continuous Dynamical Systems Using UPPAAL

AU - Schivo,Stefano

AU - Langerak,Romanus

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

KW - Euler method

KW - Model Checking

KW - Timed Automata

KW - 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

PB - Springer

ER -