Related papers: Attractors in continuous and Boolean networks
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,…
This paper refined and introduced some notations (namely attractors, physical attractors, proper attractors, topologically exact and topologically mixing) within the context of relations. We establish necessary and sufficient conditions,…
We already know a great deal about dynamical systems with uniqueness in forward time. Indeed, flows, semiflows, and maps (both invertible and not) have been studied at length. A view that has proven particularly fruitful is topological:…
This letter concerns the reliability of coupled oscillator networks in response to fluctuating inputs. Reliability means that (following a transient) an input elicits identical responses upon repeated presentations, regardless of the…
Boolean networks, inspired by gene regulatory networks, were developed to understand the complex behaviors observed in biological systems, with network attractors corresponding to biological phenotypes or cell types. In this article, we…
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…
Turbulent flows present rich dynamics originating from non-trivial energy fluxes across scales, non-stationary forcings and geometrical constraints. This complexity manifests in non-hyperbolic chaos, randomness, state-dependent persistence…
In this paper we explore the features of a graph generated by random walkers with nodes that have evolutionary attractiveness and Boltzmann-like transition probabilities that depend both on the euclidean distance between the nodes and on…
This is the second paper of a series of two about the structural properties that influence the asymptotic dynamics of Random Boolean Networks. Here we study the functionally independent clusters in which the relevant elements, introduced…
Control of the living cell functions with remarkable reliability despite the stochastic nature of the underlying molecular networks -- a property presumably optimized by biological evolution. We here ask to what extent the property of a…
Because the attractors of biological networks reflect stable behaviors (e.g., cell phenotypes), identifying control interventions that can drive a system towards its attractors (attractor control) is of particular relevance when controlling…
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…
When is it safe to approximate a complicated random Boolean network (RBN) as a simplified, easier to model RBN? When can static measures of network structure be reliably used to infer the network's dynamics? This simple experiment tests the…
Biological systems rely on robust internal information processing: Survival depends on highly reproducible dynamics of regulatory processes. Biological information processing elements, however, are intrinsically noisy (genetic switches,…
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…
We generalize the concept of basin of attraction of a stable state in order to facilitate the analysis of dynamical systems with noise and to assess stability properties of metastable states and long transients. To this end we examine the…
A Boolean network is a finite dynamical system, whose variables take values from a binary set. The value update rule for each variable is a Boolean function, depending on a selected subset of variables. Boolean networks have been widely…
Attractor dynamics are a fundamental computational motif in neural circuits, supporting diverse cognitive functions through stable, self-sustaining patterns of neural activity. In these lecture notes, we review four key examples that…
This paper presents an algorithm for approximating certain types of dynamical systems given by a system of ordinary delay differential equations by a Boolean network model. Often Boolean models are much simpler to understand than complex…
We consider a system of several nonlinear equations with a distributed delay and obtain absolute asymptotic stability conditions, independent of the delay. The ideas of the proofs are based on the notion of a strong attractor. The results…