Before revision: Regulatory dynamics has mathematical descriptions in terms of rate equations for continuous variables and, after discretization of state space and time , as Boolean maps. Here we study the effects of discretization for the notion of stability. In particular, we define the stability of a Boolean state sequence in consistency with the stability  of the original continuous trajectory that has been discretized.
After revision: Regulatory dynamics has mathematical descriptions in terms of rate equations for continuous variables and, after discretization of state space and time leads to Boolean dynamics. In the latter, the distinction between stable and unstable dynamics is usually made by checking damage after flip perturbations. Here we point out that this notion of stability is incompatible with the stability of the original continuous trajectory that has been discretized.