Related papers: Attractor and Basin Entropies of Random Boolean Ne…
We study the stability of orbits in large Boolean networks with given complex topology. We impose no restrictions on the form of the update rules, which may be correlated with local topological properties of the network. While recent past…
We generalize the poissonian evolving random graph model of Bauer and Bernard to deal with arbitrary degree distributions. The motivation comes from biological networks, which are well-known to exhibit non poissonian degree distribution. A…
Probabilistic Boolean networks (PBNs) is a widely used computational framework for modelling biological systems. The steady-state dynamics of PBNs is of special interest in the analysis of biological systems. However, obtaining the…
Asymptotic behaviors are often of particular interest when analyzing Boolean networks that represent biological systems such as signal trans- duction or gene regulatory networks. Methods based on a generalization of the steady state notion,…
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…
We present and study a probabilistic neural automaton in which the fraction of simultaneously-updated neurons is a parameter, rho (0, 1) . For small rho, there is relaxation towards one of the attractors and a great sensibility to external…
We present exact results, as well as some illustrative Monte Carlo simulations, concerning a stochastic network with weighted connections in which the fraction of nodes that are dynamically synchronized is a parameter. This allows one to…
The ability to achieve coordinated behavior --engineered or emergent-- on networked systems has attracted widespread interest over several fields. This has led to remarkable advances on the development of a theoretical understanding of the…
A basin of attraction represents the set of initial conditions leading to a specific asymptotic state of a given dynamical system. Here, we provide a classification of the most common basins found in nonlinear dynamics with the help of the…
A new strategy is introduced for estimating population size and networked population characteristics. Sample selection is based on a multi-wave snowball sampling design. A generalized stochastic block model is posited for the population's…
We deal with stochastic network simulations in a model with three distinct species that compete under cyclic rules which are similar to the rules of the popular rock-paper-scissors game. We investigate the Hamming distance density and then…
The topological structure of basin boundaries plays a fundamental role in the sensitivity to the initial conditions in chaotic dynamical systems. Herewith we present a study on the dynamics of dissipative systems close to the Hamiltonian…
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…
Observational entropy -- a quantity that unifies Boltzmann's entropy, Gibbs' entropy, von Neumann's macroscopic entropy, and the diagonal entropy -- has recently been argued to play a key role in a modern formulation of statistical…
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,…
Since their introduction, Boolean networks have been traditionally studied in view of their rich dynamical behavior under different update protocols and for their qualitative analogy with cell regulatory networks. More recently, tools…
Boolean control networks (BCNs) are discrete-time dynamical systems with Boolean state-variables and inputs that are interconnected via Boolean functions. BCNs are recently attracting considerable interest as computational models for…
We characterize synchronization phenomenon in discrete-time, discrete-state random dynamical systems, with random and probabilistic Boolean networks as particular examples. In terms of multiplicative ergodic properties of the induced linear…
Common experience suggests that attracting invariant sets in nonlinear dynamical systems are generally stable. Contrary to this intuition, we present a dynamical system, a network of pulse-coupled oscillators, in which \textit{unstable…
We propose the use of Deterministic Generalized Asynchronous Random Boolean Networks [Gershenson, 2002] as models of contextual deterministic discrete dynamical systems. We show that changes in the context have drastic effects on the global…