Stability of threshold Boolean networks

Threshold Boolean Networks (TBNs) are constructed using threshold functions that evaluate whether the input values are strong enough for the function to be either "on" or "off." In this work, we explore the properties of the dynamics of TBNs. We propose a new approach to assess the robustness of these networks while addressing the issue of multiple attractors. This method suggests the existence of a set of dominant attractors in the dynamics of TBNs, a phenomenon not commonly observed in Kauffman's networks. We demonstrate this by conducting comparative experiments between the dynamics of TBNs and Random Boolean Networks (RBNs), focusing on variations in the number of inputs per variable. Our experiments also indicate that TBNs tend to exhibit a greater number of attractors per network, though these attractors are typically shorter in length. Finally, we conduct a sensitivity analysis to examine the stability of the dominant attractors in TBNs, which shows that the dominant fixed-point attractors do not always exhibit remarkable stability across the tested size and connectivity configurations.