Canalization and the stability of NK-Kauffman networks

Boolean variables are such that they take values on Z 2 ≅ { 0 , 1 } . NK-Kauffman networks are dynamical deterministic systems of N Boolean functions that depend only on K ≤ N Boolean variables. They were proposed by Kauffman as a first step to understand cellular behavior (Kauffman, 1969) with great success. Among the problems that still have not been well understood in Kauffman networks, is the mechanism that regulates the phase transition of the system from an ordered phase where small changes of the initial state decay, to a chaotic one, where they grow exponentially. I show, that this mechanism is regulated through the irreducible decomposition of Boolean functions proposed in Zertuche (2009). This is in contrast to previous knowledge that attributed it to canalization . I also review other statistical properties of Kauffman networks that Boolean irreducibility explains.