  We investigate the dynamical behavior of simple modules composed of two genes
with two or three regulating connections. Continuous dynamics for mRNA and
protein concentrations is compared to a Boolean model for gene activity. Using
a generalized method, we study within a single framework different continuous
models and different types of regulatory functions, and establish conditions
under which the system can display stable oscillations. These conditions
concern the time scales, the degree of cooperativity of the regulating
interactions, and the signs of the interactions. Not all models that show
oscillations under Boolean dynamics can have oscillations under continuous
dynamics, and vice versa.
