Robust Set Stability of Boolean Networks: Transitioning from Initial State Sets to Targeted Destination State Sets

This paper delves into the robustness of set stability in Boolean networks, under the influence of function perturbations. Deviating from traditional notions of robust set stability, this paper concentrates on the transition from a predetermined initial set (IS) to a destination set (DS) in the context of such perturbations. It is premised on the assumption that set stability is initially achieved prior to the occurrence of function perturbations. In this setting, the concept of a reachable set is introduced and defined. Subsequently, the state space is partitioned into a number of distinct parametric sets. Criteria for robust set stabilization, specifically the transition from the IS to the DS, are developed. To validate the applicability of these established criteria, the paper includes an illustrative example.