Related papers: Exact dynamics of the critical Kauffman model with…
We study the intrinsic properties of attractors in the Boolean dynamics in complex network with scale-free topology, comparing with those of the so-called random Kauffman networks. We have numerically investigated the frozen and relevant…
This paper reviews a class of generic dissipative dynamical systems called N-K models. In these models, the dynamics of N elements, defined as Boolean variables, develop step by step, clocked by a discrete time variable. Each of the N…
We study the stable attractors of a class of continuous dynamical systems that may be idealized as networks of Boolean elements, with the goal of determining which Boolean attractors, if any, are good approximations of the attractors of…
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.…
Boolean networks have been the object of much attention, especially since S. Kauffman proposed them in the 1960's as models for gene regulatory networks. These systems are characterized by being defined on a Boolean state space and by…
We discuss the complex dynamics of a non-linear random networks model, as a function of the connectivity k between the elements of the network. We show that this class of networks exhibit an order-chaos phase transition for a critical…
This review explains in a self-contained way the properties of random Boolean networks and their attractors, with a special focus on critical networks. Using small example networks, analytical calculations, phenomenological arguments, and…
Stability is an important characteristic of network models that has implications for other desirable aspects such as controllability. The stability of a Boolean network depends on various factors, such as the topology of its wiring diagram…
Conserved dynamical systems are generally considered to be critical. We study a class of critical routing models, equivalent to random maps, which can be solved rigorously in the thermodynamic limit. The information flow is conserved for…
We present new applications of parity inversion and time-reversal to the emergence of complex behavior from simple dynamical rules in stochastic discrete models. Our parity-based encoding of causal relationships and time-reversal…
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 have been the object of much attention, especially since S. Kauffman proposed them in the 1960's as models for gene regulatory networks. These systems are characterized by being defined on a Boolean state space and by…
A model of cellular metabolism due to S. Kauffman is analyzed. It consists of a network of Boolean gates randomly assembled according to a probability distribution. It is shown that the behavior of the network depends very critically on…
Using analytic arguments, we show that dynamical attractor periods in large critical Boolean networks are power-law distributed. Our arguments are based on the method of relevant components, which focuses on the behavior of the nodes that…
Identification of attractors, that is, stable states and sustained oscillations, is an important step in the analysis of Boolean models and exploration of potential variants. We describe an approach to the search for asynchronous cyclic…
We investigate analytically and numerically the critical line in undirected random Boolean networks with arbitrary degree distributions, including scale-free topology of connections $P(k)\sim k^{-\gamma}$. We show that in infinite…
The relationship between the properties of a dynamical system and the structure of its defining equations has long been studied in many contexts. Here we study this problem for the class of conjunctive (resp. disjunctive) Boolean networks,…
Random Boolean networks were introduced in 1969 by Kauffman as a model for gene regulation. By combining analytical arguments and efficient numerical simulations, we evaluate the properties of relevant components of critical random Boolean…
We study critical random Boolean networks with two inputs per node that contain only canalyzing functions. We present a phenomenological theory that explains how a frozen core of nodes that are frozen on all attractors arises. This theory…
Biological processes, including cell differentiation, organism development, and disease progression, can be interpreted as attractors (fixed points or limit cycles) of an underlying networked dynamical system. In this paper, we study the…