Dynamical Instability in Boolean Networks as a Percolation Problem pdf

Phase Transitions in Complex Network Dynamics

A connection between the percolation transition and the onset of chaos in the Kauffman model

Percolation and spreading of damage in a simplified Kauffman model

Activities and Sensitivities in Boolean Network Models

Core Percolation and Onset of Complexity in Boolean Networks

Annealed approximation: Random Networks of Automata: A Simple Annealed Approximation

Boolean functions in Boolean networks are represented by a truth table, that in turn can be represented by a $2^K$-length vector/string of $0$s and $1$s, for a $K$-input truth table. $2^K$ is the number of possible inputs, i.e. the cardinality of the set $\{1,0\}^K$. The bit string can be interpreted as a binary decision tree.

Activities and Sensitivities in Boolean Network Models

The average sensitivity (when averaged over all the functions in the network) appears to be a good parameter for predicting whether the dynamics of the Boolean network are ordered or chaotic

Activities and Sensitivities in Boolean Network Models

Random Boolean networks: Analogy with percolation (Stauffer)

Some interesting analogies, investigated via computer simulations, between percolation and properties of Kauffman Boolean networks in a 2D lattice

Random Boolean networks: Analogy with percolation

Connection between sensitivity and complexity of GP map of Boolean networks.. MMathPhys oral presentation

Relation between Kolmogorov complexity and sensitivity of a Boolean function.

Sensitivity <> constrained/unconstrained, coding/non-coding, etc.

More references:

A geometrical interpretation of the chaotic state of inhomogeneous deterministic cellular automata The role of certain Post classes in Boolean network models of genetic networks Boolean Dynamics with Random Couplings Isomorphism of Quasispecies and Percolation Models Spectral theory for the robustness and dynamical properties of complex networks Phase Transitions in Two-Dimensional Kauffman Cellular Automata Phase transition in cellular random Boolean nets The Physics of Structure Formation: Theory and Simulation