相关论文: Exact dynamics of the critical Kauffman model with…

The Kauffman model describes a system of randomly connected nodes with dynamics based on Boolean update functions. Though it is a simple model, it exhibits very complex behavior for "critical" parameter values at the boundary between a…

The Kauffman model of genetic computation highlights the importance of criticality at the border of order and chaos. The model with connectivity one is of special interest because it is exactly solvable. But our understanding of its…

The Kauffman model is the archetypal model of genetic computation. It highlights the importance of criticality, at which many biological systems seem poised. In a series of advances, researchers have honed in on how the number of attractors…

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…

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…

Random Boolean networks, originally invented as models of genetic regulatory networks, are simple models for a broad class of complex systems that show rich dynamical structures. From a biological perspective, the most interesting networks…

We study two types of simple Boolean networks, namely two loops with a cross-link and one loop with an additional internal link. Such networks occur as relevant components of critical K=2 Kauffman networks. We determine mostly analytically…

We show that the mean number of attractors in a critical Boolean network under asynchronous stochastic update grows like a power law and that the mean size of the attractors increases as a stretched exponential with the system size. This is…

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 derive mostly analytically the scaling behavior of the number of nonfrozen and relevant nodes in critical Kauffman networks (with two inputs per node) in the thermodynamic limit. By defining and analyzing a stochastic process that…

The evaluation of the number of attractors in Kauffman networks by Samuelsson and Troein is generalized to critical networks with one input per node and to networks with two inputs per node and different probability distributions for update…

This is the first of two papers about the structure of Kauffman networks. In this paper we define the relevant elements of random networks of automata, following previous work by Flyvbjerg and Flyvbjerg and Kjaer, and we study numerically…

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…

Kauffman net is a dynamical system of logical variables receiving two random inputs and each randomly assigned a boolean function. We show that the attractor and transient lengths exhibit scaleless behavior with power-law distributions over…

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…

Effective control of biological systems can often be achieved through the control of a surprisingly small number of distinct variables. We bring clarity to such results using the formalism of Boolean dynamical networks, analyzing the…

We investigate the influence of a deterministic but non-synchronous update on Random Boolean Networks, with a focus on critical networks. Knowing that ``relevant components'' determine the number and length of attractors, we focus on such…

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…

We investigate Threshold Random Boolean Networks with $K = 2$ inputs per node, which are equivalent to Kauffman networks, with only part of the canalyzing functions as update functions. According to the simplest consideration these networks…

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…