Related papers: Counting attractors in synchronously updated rando…
We consider Boolean networks with interaction graphs partitioned into strongly connected components, which we call strong modules. This type of network decomposition has been considered in the literature, primarily from the perspective of…
In this review, we describe the singular success of attractor neural network models in describing how the brain maintains persistent activity states for working memory, error-corrects, and integrates noisy cues. We consider the mechanisms…
We investigate the influence of a deterministic but non-synchronous update on Random Boolean Networks, with a focus on critical networks. Knowing that ``relevant components'' determine the number and length of attractors, we focus on such…
The understanding of Boolean automata networks dynamics takes an important place in various domains of computer science such as computability, complexity and discrete dynamical systems. In this paper, we make a step further in this…
Attractors of dynamical systems may be networks in phase space that can be heteroclinic (where there are dynamical connections between simple invariant sets) or excitable (where a perturbation threshold needs to be crossed to a dynamical…
We study the class of cooperative Boolean networks whose only regulatory functions are COPY, binary AND, and binary OR. We prove that for all sufficiently large N and c < 2 there exist Boolean networks in this class that have an attractor…
The random map model is a deterministic dynamical system in a finite phase space with n points. The map that establishes the dynamics of the system is constructed by randomly choosing, for every point, another one as being its image. We…
The relationship between the properties of a dynamical system and the structure of its defining equations has long been studied in many contexts. Here we study this problem for the class of conjunctive (resp. disjunctive) Boolean networks,…
Boolean networks model finite discrete dynamical systems with complex behaviours. The state of each component is determined by a Boolean function of the state of (a subset of) the components of the network. This paper addresses the…
We study the target control problem of asynchronous Boolean networks, to identify a set of nodes, the perturbation of which can drive the dynamics of the network from any initial state to the desired steady state (or attractor). We are…
Boolean networks is a well-established formalism for modelling biological systems. A vital challenge for analysing a Boolean network is to identify all the attractors. This becomes more challenging for large asynchronous Boolean networks,…
We show that synchronism can significantly impact on network behaviours, in particular by filtering unstable attractors induced by a constraint of asynchronism. We investigate and classify the different possible impacts that an addition of…
Boolean networks are popular tools for the exploration of qualitative dynamical properties of biological systems. Several dynamical interpretations have been proposed based on the same logical structure that captures the interactions…
The problem of reliability of the dynamics in biological regulatory networks is studied in the framework of a generalized Boolean network model with continuous timing and noise. Using well-known artificial genetic networks such as the…
Asynchronous Boolean networks are a type of discrete dynamical system in which each variable can take one of two states, and a single variable state is updated in each time step according to pre-selected rules. Boolean networks are popular…
Chaotic functions are characterized by sensitivity to initial conditions, transitivity, and regularity. Providing new functions with such properties is a real challenge. This work shows that one can associate with any Boolean network a…
Biological processes, including cell differentiation, organism development, and disease progression, can be interpreted as attractors (fixed points or limit cycles) of an underlying networked dynamical system. In this paper, we study the…
Complex systems are often modeled as Boolean networks in attempts to capture their logical structure and reveal its dynamical consequences. Approximating the dynamics of continuous variables by discrete values and Boolean logic gates may,…
Boolean automata networks (aka Boolean networks) are space-time discrete dynamical systems, studied as a model of computation and as a representative model of natural phenomena. A collection of simple entities (the automata) update their…
Disorder and noise in physical systems often disrupt spatial and temporal regularity, yet chaotic systems reveal how order can emerge from unpredictable behavior. Complex networks, spatial analogs of chaos, exhibit disordered, non-Euclidean…