Stability of linear Boolean networks

Stability is an important characteristic of network models that has implications for other desirable aspects such as controllability. The stability a Boolean depends on various factors, the topology its wiring diagram and type functions describing dynamics. In this paper, we study linear networks by computing Derrida curves quantifying number attractors cycle lengths imposed their topologies. are commonly used to measure several parameters average in-degree K output bias p can indicate if stable, critical, or unstable. For random unbiased there critical connectivity value Kc=2 KKc chaotic regime. Here, show networks, which least canalizing most unstable, phase transition from order chaos already happens at Kc=1. Consistently, also unstable exhibit large with very long limit cycles while stable fewer shorter cycles. Additionally, present theoretical results quantify dynamical properties networks. First, formula proportion attractor states systems. Second, expected fixed points systems 2, general possess one point. Third, bijective provide lower bound percentage network.