Dynamical attraction in parallel network models

摘要

In this work, we give a characterization of attractors in parallel deterministic network models, which evolve by means of maxterm and minterm Boolean functions and provide a method to obtain their basins of attraction. In order to do that, we distinguish the two possible cases: attractive fixed points and attractive 2-periodic orbits. Furthermore, we state necessary and sufficient conditions to know when a fixed point or a 2-periodic orbit is globally attractive. This makes possible to obtain a detailed description of their phase diagrams. Besides, we provide optimal upper bounds for the transient in such models, i.e., for the maximum number of iterations required to reach one of the periodic orbits. Moreover, we establish patterns that allow us to obtain a PDS on a maxterm or minterm Boolean function for which any given optimal upper bound for the transient is reached.