Related papers: Relevant elments, Magnetization and Dynamical Prop…
The growth in number and nature of dynamical attractors in Kauffman NK network models are still not well understood properties of these important random boolean networks. Structural circuits in the underpinning graph give insights into the…
We study a dynamical random network model in which at every construction step a new vertex is introduced and attached to every existing vertex independently with a probability proportional to a concave function f of its current degree. We…
We provide a framework for determining the centralities of agents in a broad family of random networks. Current understanding of network centrality is largely restricted to deterministic settings, but practitioners frequently use random…
The research concerns the dynamics of complex autonomous Kauffman networks. The article defines and shows using simulation experiments half-chaotic networks, which exhibit features much more similar to typically modeled systems like a…
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 show that to correctly describe the position of the critical line in the Kauffman random boolean networks one must take into account percolation phenomena underlying the process of damage spreading. For this reason, since the issue of…
The Kauffman model describes a particularly simple class of random Boolean networks. Despite the simplicity of the model, it exhibits complex behavior and has been suggested as a model for real world network problems. We introduce a novel…
The combination of the compactness of networks, featuring small diameters, and their complex architectures results in a variety of critical effects dramatically different from those in cooperative systems on lattices. In the last few years,…
We describe systems using Kauffman and similar networks. They are directed funct ioning networks consisting of finite number of nodes with finite number of discr ete states evaluated in synchronous mode of discrete time. In this paper we…
The random map model is a deterministic dynamical system in a finite phase space with n points. The map that establishes the dynamics of the system is constructed by randomly choosing, for every point, another one as being its image. We…
We study the family of network models derived by requiring the expected properties of a graph ensemble to match a given set of measurements of a real-world network, while maximizing the entropy of the ensemble. Models of this type play the…
The exponential family of random graphs is one of the most promising class of network models. Dependence between the random edges is defined through certain finite subgraphs, analogous to the use of potential energy to provide dependence…
We derive analytically the scaling behavior in the thermodynamic limit of the number of nonfrozen and relevant nodes in the most general class of critical Kauffman networks for any number of inputs per node, and for any choice of the…
Real-world complex systems such as ecological communities and neuron networks are essential parts of our everyday lives. These systems are composed of units which interact through intricate networks. The ability to predict sudden changes in…
We present an analytic formalism describing structural properties of random uncorrelated networks with arbitrary degree distributions. The formalism allows to calculate the main network characteristics like: the position of the phase…
We study how the dynamics of a class of discrete dynamical system models for neuronal networks depends on the connectivity of the network. Specifically, we assume that the network is an Erd\H{o}s-R\'{enyi} random graph and analytically…
An account is given of the features, of the kind pertaining to q-statistics, of the dynamics at the one-dimensional critical attractors associated to the three familiar routes to chaos, intermittency, period doubling and quasiperiodicity.…
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…
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…
This paper presents a new chaotic system having four attractors, including two fixed point attractors and two symmetrical chaotic strange attractors. Dynamical properties of the system, viz. sensitive dependence on initial conditions,…