Viability theory
Parameterized polyhedra and their vertices
International Journal of Parallel Programming
Timing analysis of asynchronous circuits using timed automata
CHARME '95 Proceedings of the IFIP WG 10.5 Advanced Research Working Conference on Correct Hardware Design and Verification Methods
Towards Computing Phase Portraits of Polygonal Differential Inclusions
HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
Semantics of Biological Regulatory Networks
Electronic Notes in Theoretical Computer Science (ENTCS)
Analysing formal models of genetic regulatory networks with delays
International Journal of Bioinformatics Research and Applications
On timed models of gene networks
FORMATS'07 Proceedings of the 5th international conference on Formal modeling and analysis of timed systems
Incorporating time delays into the logical analysis of gene regulatory networks
CMSB'06 Proceedings of the 2006 international conference on Computational Methods in Systems Biology
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The analysis of Biological Regulatory Network (BRN) leads to the computing of the set of the possible behaviours of the biological components. These behaviours are seen as trajectories and we are specifically interested in cyclic trajectories since they stand for stability. The set of cycles is given by the so-called invariance kernel of a BRN. This paper presents a method for deriving symbolic formulae for the length, volume and diameter of a cylindrical invariance kernel. These formulae are expressed in terms of delay parameters expressions and give the existence of an invariance kernel and a hint of the number of cyclic trajectories.