ABSTRACT
In cases where the same real-world system can be modeled both by an ODE system â and a Boolean system ð¹, it is of interest to identify conditions under which the two systems will be consistent, that is, will make qualitatively equivalent predictions. In this note we introduce two broad classes of relatively simple models that provide a convenient framework for studying such questions. In contrast to the widely known class of Glass networks, the right-hand sides of our ODEs are Lipschitz-continuous. We prove that if ð¹ has certain structures, consistency between â and ð¹ is implied by sufficient separation of time scales in one class of our models. Namely, if the trajectories of ð¹ are "one-stepping" then we prove a strong form of consistency and if ð¹ has a certain monotonicity property then there is a weaker consistency between â and ð¹. These results appear to point to more general structure properties that favor consistency between ODE and Boolean models.
