Related papers: The Modular Structure of Kauffman Networks
In this work, we study the topological transition on the associated networks in a model proposed by Saeedian et al. (Scientific Reports 2019 9:9726), which considers a coupled dynamics of node and link states. Our goal was to better…
Clustering, assortativity, and communities are key features of complex networks. We probe dependencies between these attributes and find that ensembles with strong clustering display both high assortativity by degree and prominent community…
Boolean networks, first developed in the late 1960s as a tool for studying complex disordered dynamical systems, consist of nodes governed by Boolean functions whose evolution is entirely deterministic in that the state of the network at a…
We give a physical description in terms of percolation theory of the phase transition that occurs when the disorder increases in the random antiferromagnetic spin-1 chain between a gapless phase with topological order and a random singlet…
Starting with a percolation model in $\Z^d$ in the subcritical regime, we consider a random walk described as follows: the probability of transition from $x$ to $y$ is proportional to some function $f$ of the size of the cluster of $y$.…
Random Threshold Networks with sparse, asymmetric connections show complex dynamical behavior similar to Random Boolean Networks, with a transition from ordered to chaotic dynamics at a critical average connectivity $K_c$. In this type of…
To model biological systems using networks, it is desirable to allow more than two levels of expression for the nodes and to allow the introduction of parameters. Various modeling and simulation methods addressing these needs using Boolean…
In this work, we investigate a model of an adaptive networked dynamical system, where the coupling strengths among phase oscillators coevolve with the phase states. It is shown that in this model the oscillators can spontaneously…
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…
In this work, several random Boolean networks (RBN) are generated and analyzed from two characteristics: their time evolution diagram and their transition diagram. For this purpose, its randomness is estimated using three measures, of which…
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical…
We discuss basic features of emergent complexity in dynamical systems far from equilibrium by focusing on the network structure of their state space. We start by measuring the distributions of avalanche and transient times in Random Boolean…
Boolean networks have been widely used in many areas of science and engineering to represent various dynamical behaviour. In systems biology, they became useful tools to study the dynamical characteristics of large-scale biomolecular…
We study the properties of the distance between attractors in Random Boolean Networks, a prominent model of genetic regulatory networks. We define three distance measures, upon which attractor distance matrices are constructed and their…
Boolean networks are a popular modeling framework in computational biology to capture the dynamics of molecular networks, such as gene regulatory networks. It has been observed that many published models of such networks are defined by…
Percolation theory allows simple description of the phase transition based on the scaling properties of the network clusters with respect to a single parameter - site or bond occupation probability. How to design a network exhibiting the…
In automata networks, it is well known that the way entities update their states over time has a major impact on their dynamics. In particular, depending on the chosen update schedule, the underlying dynamical systems may exhibit more or…
In this report, we present a formal approach that addresses the problem of emergence of phase transitions in stochastic and attractive nonlinear threshold Boolean automata networks. Nonlinear networks considered are informally defined on…
Our daily social and political life is more and more impacted by social networks. The functioning of our living bodies is deeply dependent on biological regulation networks such as neural, genetic, and protein networks. And the physical…
We introduce a model for the formation of social networks, which takes into account the homophily or the tendency of individuals to associate and bond with similar others, and the mechanisms of global and local attachment as well as tie…