Threshold network dynamic systems and applications

Abstract

Recent mathematical developments in an important class of automata networks is outlined. The study is focused on the threshold networks. Developing discrete-time iterative inequalities and energy/Lyapunov function approach, comparison results for discrete-time iterative process under environmental and Markovian perturbations are established. Using the comparison results, the qualitative properties of both stochastic and deterministic automata networks are analyzed. Several applications are given to illustrates the usefulness of the results.