Synchronization of pulse-coupled biological oscillators
SIAM Journal on Applied Mathematics
Specifying real-time properties with metric temporal logic
Real-Time Systems
Journal of the ACM (JACM)
Theoretical Computer Science
Symbolic model checking for real-time systems
Information and Computation
Proceedings of the DIMACS/SYCON workshop on Hybrid systems III : verification and control: verification and control
HART '97 Proceedings of the International Workshop on Hybrid and Real-Time Systems
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CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
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CAV '94 Proceedings of the 6th International Conference on Computer Aided Verification
Model-Checking for Real-Time Systems
FCT '95 Proceedings of the 10th International Symposium on Fundamentals of Computation Theory
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Sync: The Emerging Science of Spontaneous Order
Sync: The Emerging Science of Spontaneous Order
The temporal logic of programs
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
Model Checking Biological Oscillators
Electronic Notes in Theoretical Computer Science (ENTCS)
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We define a subclass of timed automata, called oscillator timed automata, suitable to model biological oscillators. Coupled biological oscillators may synchronise, as emerging behaviour, after a period of time in which they interact through physical or chemical means. We introduce a parametric semantics for their interaction that is general enough to capture the behaviour of different types of oscillators. We instantiate it both to the Kuramoto model, a model of synchronisation based on smooth interaction, and to the Peskin model of pacemaker cells in the heart, a model of synchronisation based on pulse interaction. We also introduce a logic, Biological Oscillators Synchronisation Logic (BOSL), that is able to describe collective synchronisation properties of a population of coupled oscillators. A model checking algorithm is proposed for the defined logic and it is implemented in a model checker. The model checker can be used to detect synchronisation properties of a given population of oscillators. This tool might be the basic step towards the generation of suitable techniques to control and regulate the behaviour of coupled oscillators in order to ensure the reachability of synchronisation.