Related papers: Self-Organized Critical Random Boolean Networks
Boolean networks (BNs) are discrete-time systems where nodes are inter-connected (here we call such connection rule among nodes as network structure), and the dynamics of each gene node is determined by logical functions. In this paper, we…
We consider critical phenomena on heterogeneous small-world networks having a scale-free character but also arbitrary short-loops. After deriving the self-consistent equation for the order parameter and the critical surface, we prove that…
Information processing in complex systems is often found to be maximally efficient close to critical states associated with phase transitions. It is therefore conceivable that also neural information processing operates close to…
Self-organized criticality has been proposed to be a universal mechanism for the emergence of scale-free dynamics in many complex systems, and possibly in the brain. While such scale-free patterns were identified experimentally in many…
Asynchronous irregular (AI) and critical states are two competing frameworks proposed to explain spontaneous neuronal activity. Here, we propose a mean-field model with simple stochastic neurons that generalizes the integrate-and-fire…
Autonomous randomly coupled neural networks display a transition to chaos at a critical coupling strength. We here investigate the effect of a time-varying input on the onset of chaos and the resulting consequences for information…
The presence of both critical behavior and oscillating patterns in brain dynamics is a very interesting issue. In this paper, we consider a model for a neuron population, where each neuron is modeled by an over-damped rotator. We find that…
To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisfied for the transitions between topological states. This enables…
We consider a network, bonds of which are being sequentially removed; that is done at random, but conditioned on the system remaining connected (Self-Repairing Bond Percolation SRBP). This model is the simplest representative of a class of…
This paper studies a stylized model of local interaction where agents choose from an ever increasing set of vertically ranked actions, e.g. technologies. The driving forces of the model are infrequent upward shifts (``updates''), followed…
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…
$k$-Core percolation has served as a paradigmatic model of discontinuous percolation for a long time. Recently it was revealed that the order parameter of $k$-core percolation of random networks additionally exhibits critical behavior. Thus…
This paper presents a unified framework for analyzing the input-output behavior of discrete time complex networks viewed as open systems. Importantly, we focus on systems that are inherently modeled in discrete time-such as opinion…
We study the Ising model in a hierarchical small-world network by renormalization group analysis, and find a phase transition between an ordered phase and a critical phase, which is driven by the coupling strength of the shortcut edges.…
In this paper, a nonlinear system aiming at reducing the signal transmission rate in a networked control system is constructed by adding nonlinear constraints to a linear feedback control system. Its stability is investigated in detail. It…
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,…
A new analytical framework consisting of two phenomena: single sample and multiple samples, is proposed to deal with the identification problem of Boolean control networks (BCNs) systematically and comprehensively. Under this framework, the…
Networks in the real world do not exist as isolated entities, but they are often part of more complicated structures composed of many interconnected network layers. Recent studies have shown that such mutual dependence makes real networked…
The controllability of networked sampled-data systems with zero-order holders on the control and transmission channels is explored, where single- and multi-rate sampling patterns are considered, respectively. The effects of sampling on the…
A sandpile model with stochastic toppling rule is studied. The control parameters and the phase diagram are determined through a MF approach, the subcritical and critical regions are analyzed. The model is found to have some similarities…