Related papers: Attractor separation and signed cycles in asynchro…
Despite their apparent simplicity, random Boolean networks display a rich variety of dynamical behaviors. Much work has been focused on the properties and abundance of attractors. We here derive an expression for the number of attractors in…
Identification of attractors, that is, stable states and sustained oscillations, is an important step in the analysis of Boolean models and exploration of potential variants. We describe an approach to the search for asynchronous cyclic…
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,…
We present a computational method for finding attractors (ergodic sets of states) of Boolean networks under asynchronous update. The approach is based on a systematic removal of state transitions to render the state transition graph…
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…
Despite their apparent simplicity, random Boolean networks display a rich variety of dynamical behaviors. Much work has been focused on the properties and abundance of attractors. The topologies of random Boolean networks with one input per…
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 consider the following question on the relationship between the asymptotic behaviours of asynchronous dynamics of Boolean networks and their regulatory structures: does the presence of a cyclic attractor imply the existence of a local…
This paper addresses the problem of finding cycles in the state transition graphs of synchronous Boolean networks. Synchronous Boolean networks are a class of deterministic finite state machines which are used for the modeling of gene…
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…
There are few examples of non-autonomous vector fields exhibiting complex dynamics that may be proven analytically. We analyse a family of periodic perturbations of a weakly attracting robust heteroclinic network defined on the two-sphere.…
The combination of complex networks and dynamic systems research is poised to yield some of the most interesting theoretic and applied scientific results along the forthcoming decades. The present work addresses a particularly important…
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…
Results and tools on discrete interaction networks are often concerned with Boolean variables, whereas considering more than two levels is sometimes useful. Multivalued networks can be converted to partial Boolean maps, in a way that…
We study the stable attractors of a class of continuous dynamical systems that may be idealized as networks of Boolean elements, with the goal of determining which Boolean attractors, if any, are good approximations of the attractors of…
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,…
We are interested in the relationships between the number fixed points in a Boolean network $f:\{0,1\}^n\to\{0,1\}^n$ and its interaction graph, which is the arc-signed digraph $G$ on $\{1,\dots,n\}$ that describes the positive and negative…
We study Boolean networks which are simple spatial models of the highly conserved Delta-Notch system. The models assume the inhibition of Delta in each cell by Notch in the same cell, and the activation of Notch in presence of Delta in…
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…
Combinatorial threshold-linear networks (CTLNs) are a special class of inhibition-dominated TLNs defined from directed graphs. Like more general TLNs, they display a wide variety of nonlinear dynamics including multistability, limit cycles,…