The Importance of Being (A Little Bit) Discrete

We compare the hybrid, stochastic, and differential semantics for stochastic Concurrent Constraint Programming, focussing on the exhibited behavior of models and their robustness. By investigating in detail two case studies, a circadian clock model and the Repressilator, we comment on the effect of the introduction of a limited amount of discreteness in the description of biological systems with hybrid automata. Experimental evidence suggests that discreteness increases robustness of the models.