Related papers: Cooperative Boolean systems with generically long …
Continuous-time systems with switch-like behaviour occur in chemical kinetics, gene regulatory networks and neural networks. Networks with hard switching, as a limiting case of smooth sigmoidal switching, retain the richest possible range…
Canalization is a classic concept in Developmental Biology that is thought to be an important feature of evolving systems. In a Boolean network it is a form of network robustness in which a subset of the input signals control the behavior…
We study the target control of asynchronous Boolean networks, to identify efficacious interventions that can drive the dynamics of a given Boolean network from any initial state to the desired target attractor. Based on the application…
Models of biochemical networks are frequently high-dimensional and complex. Reduction methods that preserve important dynamical properties are therefore essential in their study. Interactions between the nodes in such networks are…
Global dynamics of a non-linear Cellular Automata is, in general irregular, asymmetric and unpredictable as opposed to that of a linear CA, which is highly systematic and tractable. In the past efforts have been made to systematize…
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…
A broad range of nonlinear processes over networks are governed by threshold dynamics. So far, existing mathematical theory characterizing the behavior of such systems has largely been concerned with the case where the thresholds are…
We investigate the phenomenon of diffusion in a countably infinite society of individuals interacting with their neighbors in a network. At a given time, each individual is either active or inactive. The diffusion is driven by two…
We study the dynamics of randomly connected networks composed of binary Boolean elements and those composed of binary majority vote elements. We elucidate their differences in both sparsely and densely connected cases. The quickness of…
Boolean networks are powerful frameworks for capturing the logic of gene-regulatory circuits, yet their combinatorial explosion hampers exhaustive analyses. Here, we present a systematic reduction of a 31-node Boolean model that describes…
We introduce the Cooperative Network Architecture (CNA), a model that represents sensory signals using structured, recurrently connected networks of neurons, termed "nets." Nets are dynamically assembled from overlapping net fragments,…
We study the behavior of a generalized consensus dynamics on a temporal network of interactions, the activity driven network with attractiveness. In this temporal network model, agents are endowed with an intrinsic activity $a$, ruling the…
The generating functional method is employed to investigate the synchronous dynamics of Boolean networks, providing an exact result for the system dynamics via a set of macroscopic order parameters. The topology of the networks studied and…
Gene regulatory networks can be successfully modeled as Boolean networks. A much discussed hypothesis says that such model networks reproduce empirical findings the best if they are tuned to operate at criticality, i.e. at the borderline…
Study of network dynamics is very active area in biological and social sciences. However, the relationship between the network structure and the attractors of the dynamics has not been fully understood yet. In this study, we numerically…
First, the topological structure of a transition system is studied. Then, two types of transition system (TS) representations of Boolean networks (BNs) and Boolean control networks (BCNs) are investigated. The first kind of representation…
The Boolean autonomous dynamical systems, also called regular autonomous asynchronous systems are systems whose 'vector field' is a function {\Phi}:{0,1}^{n}{\to}{0,1}^{n} and time is discrete or continuous. While the synchronous systems…
We present a rigorous mathematical framework for analyzing dynamics of a broad class of Boolean network models. We use this framework to provide the first formal proof of many of the standard critical transition results in Boolean network…
Boolean circuits abstract away from physical details to focus on the logical structure and computational behaviour of digital components. Although such circuits have been studied for many decades, compositionality has been widely ignored or…
Boolean networks are discrete dynamical systems for modeling regulation and signaling in living cells. We investigate a particular class of Boolean functions with inhibiting inputs exerting a veto (forced zero) on the output. We give…