Related papers: Counting attractors in synchronously updated rando…
Using analytic arguments, we show that dynamical attractor periods in large critical Boolean networks are power-law distributed. Our arguments are based on the method of relevant components, which focuses on the behavior of the nodes that…
Observing the internal state of the whole system using a small number of sensor nodes is important in analysis of complex networks. Here, we study the problem of determining the minimum number of sensor nodes to discriminate attractors…
This paper details a method for optimising the size of Boolean automata networks in order to compute their attractors under the parallel update schedule. This method relies on the formalism of modules introduced recently that allows for…
To simplify the analysis of Boolean networks, a reduction in the number of components is often considered. A popular reduction method consists in eliminating components that are not autoregulated, using variable substitution. In this work,…
Effective control of biological systems can often be achieved through the control of a surprisingly small number of distinct variables. We bring clarity to such results using the formalism of Boolean dynamical networks, analyzing the…
It is known that there are no more Lyndon words of length n than there are periodic necklaces of same length. This paper considers a similar problem where, additionally, the necklaces must be without some forbidden factors. This problem…
The deterministic dynamics of randomly connected neural networks are studied, where a state of binary neurons evolves according to a discreet-time synchronous update rule. We give a theoretical support that the overlap of systems' states…
Previous work in Boolean dynamical networks has suggested that the number of components that must be controlled to select an existing attractor is typically set by the number of attractors admitted by the dynamics, with no dependence on the…
In this paper, we give some results concerning the dynamics of double Boolean automata circuits (dbac's for short), namely, networks associated to interaction graphs composed of two side-circuits that share a node. More precisely, we give…
To model biological systems using networks, it is desirable to allow more than two levels of expression for the nodes and to allow the introduction of parameters. Various modeling and simulation methods addressing these needs using Boolean…
Discrete dynamical systems in which model components take on categorical values have been successfully applied to biological networks to study their global dynamic behavior. Boolean models in particular have been used extensively. However,…
It is an increasingly important problem to study conditions on the structure of a network that guarantee a given behavior for its underlying dynamical system. In this paper we report that a Boolean network may fall within the chaotic…
Boolean networks are special types of finite state time-discrete dynamical systems. A Boolean network can be described by a function from an n-dimensional vector space over the field of two elements to itself. A fundamental problem in…
We study classes of dynamical systems that can be obtained by constructing recursive networks with monotone Boolean functions. Stack filters in nonlinear signal processing are special cases of such systems. We show an analytical connection…
Boolean networks are a valuable class of discrete dynamical systems models, but they remain fundamentally limited by their inability to capture multi-way interactions in their components. To remedy this limitation, we propose a model of…
In this paper we study the dynamical behavior of Boolean networks with firing memory, namely Boolean networks whose vertices are updated synchronously depending on their proper Boolean local transition functions so that each vertex remains…
We clarify the effect different sampling methods and weighting schemes have on the statistics of attractors in ensembles of random Boolean networks (RBNs). We directly measure cycle lengths of attractors and sizes of basins of attraction in…
The critical Kauffman model with connectivity one is the simplest class of critical Boolean networks. Nevertheless, it exhibits intricate behavior at the boundary of order and chaos. We introduce a formalism for expressing the dynamics of…
In previous works, we introduced the notion of dominant vertices in the context of dynamical systems on networks. This is a set of nodes in the underlying network whose evolution determines the whole network's dynamics after a transient…
We show that the mean number of attractors in a critical Boolean network under asynchronous stochastic update grows like a power law and that the mean size of the attractors increases as a stretched exponential with the system size. This is…