A Random Boolean Network shifted toward a critical point

Abstract

Abstract Random Boolean Networks (RBNs) model complex networks with numerous variables, serving as a tool for gene expression and genetic regulation modeling. RBNs exhibit phase transitions, contingent on node degrees. Given the significance of phase transitions in collective behaviors, the study explores the relationship between RBNs and actual living system networks, which also display critical behaviors. Notably, living systems exhibit such behaviors even beyond the predicted critical point in RBNs. This paper introduces a novel RBNs model incorporating a rewiring process for edge connections/disconnections. In contrast to prior studies, our model includes artificial genes occasionally adding self-loops and creating an instant and temporal lookup table. Consequently, our proposed model demonstrates the edge of chaos at higher node degrees. It serves as an abstract RBNs model generating noisy behaviors from internal agent processes without external parameter tuning.