Transient Perturbations on Scale-Free Boolean Networks with Topology Driven Dynamics

2011 ◽  
pp. 337-344
Author(s):  
Christian Darabos ◽  
Mario Giacobini ◽  
Marco Tomassini
Keyword(s):  
Boolean Networks ◽  
Scale Free

scholarly journals Critical Boolean networks with scale-free in-degree distribution

2009 ◽  
Vol 80 (2) ◽  
Author(s):  
Barbara Drossel ◽  
Florian Greil
Keyword(s):  
Degree Distribution ◽  
Boolean Networks ◽  
Scale Free

Influence of reciprocal links on the dynamics of scale-free Boolean networks

2020 ◽  
Vol 31 (03) ◽  
pp. 2050040
Author(s):  
Luca Agostini
Keyword(s):  
Numerical Simulation ◽  
Direct Effect ◽  
Network Size ◽  
Boolean Networks ◽  
Average Degree ◽  
Scale Free ◽  
Kauffman Model ◽  
Dynamical Properties

We study the effects of the reciprocal links on the dynamics of direct Boolean networks with scale-free topology (SFRBNs). By means of the method of the Derrida Plot, we have investigated the SFRBNs characterized by different values of average degree and different values of reciprocity in order to test the behavioral regimes of the system. The following step was to perform numerical simulation with the quenched Kauffman model to study the dynamical properties of critical SFRBNs with [Formula: see text]. The distribution of the number of different attractors, the period of the cyclic attractors, the transient duration and the fraction of the frozen nodes, have been studied as a function of the reciprocity and network size. The results presented reveal that reciprocity seems to have no direct effect on the changing of the behavioral regime of SFRBNs with given value of [Formula: see text]. On the contrary, we observed that reciprocal links have a profound effect on the dynamic of critical SFRBNs.

On the dynamics of random Boolean networks with scale-free outgoing connections

2004 ◽  
Vol 339 (3-4) ◽  
pp. 665-673 ◽  
Author(s):  
Roberto Serra ◽  
Marco Villani ◽  
Luca Agostini
Keyword(s):  
Boolean Networks ◽  
Scale Free ◽  
Random Boolean Networks

Generalized Boolean Networks

2010 ◽  
pp. 429-449 ◽  
Author(s):  
Christian Darabos ◽  
Mario Giacobini ◽  
Marco Tomassini
Keyword(s):  
Biological Networks ◽  
Regulatory Networks ◽  
Dynamical Behavior ◽  
Real Life ◽  
Network Models ◽  
Cell Types ◽  
Boolean Networks ◽  
Genetic Regulatory Networks ◽  
Point Of View ◽  
Scale Free

Random Boolean Networks (RBN) have been introduced by Kauffman more than thirty years ago as a highly simplified model of genetic regulatory networks. This extremely simple and abstract model has been studied in detail and has been shown capable of extremely interesting dynamical behavior. First of all, as some parameters are varied such as the network’s connectivity, or the probability of expressing a gene, the RBN can go through a phase transition, going from an ordered regime to a chaotic one. Kauffman’s suggestion is that cell types correspond to attractors in the RBN phase space, and only those attractors that are short and stable under perturbations will be of biological interest. Thus, according to Kauffman, RBN lying at the edge between the ordered phase and the chaotic phase can be seen as abstract models of genetic regulatory networks. The original view of Kauffman, namely that these models may be useful for understanding real-life cell regulatory networks, is still valid, provided that the model is updated to take into account present knowledge about the topology of real gene regulatory networks, and the timing of events, without loosing its attractive simplicity. According to present data, many biological networks, including genetic regulatory networks, seem, in fact, to be of the scale-free type. From the point of view of the timing of events, standard RBN update their state synchronously. This assumption is open to discussion when dealing with biologically plausible networks. In particular, for genetic regulatory networks, this is certainly not the case: genes seem to be expressed in different parts of the network at different times, according to a strict sequence, which depends on the particular network under study. The expression of a gene depends on several transcription factors, the synthesis of which appear to be neither fully synchronous nor instantaneous. Therefore, we have recently proposed a new, more biologically plausible model. It assumes a scale-free topology of the networks and we define a suitable semi-synchronous dynamics that better captures the presence of an activation sequence of genes linked to the topological properties of the network. By simulating statistical ensembles of networks, we discuss the attractors of the dynamics, showing that they are compatible with theoretical biological network models. Moreover, the model demonstrates interesting scaling abilities as the size of the networks is increased.

scholarly journals STRUCTURAL TENDENCIES — EFFECTS OF ADAPTIVE EVOLUTION OF COMPLEX (CHAOTIC) SYSTEMS

2008 ◽  
Vol 19 (04) ◽  
pp. 647-664 ◽  
Author(s):  
ANDRZEJ GECOW
Keyword(s):  
Finite Number ◽  
Adaptive Evolution ◽  
Boolean Networks ◽  
Network Growth ◽  
Synchronous Mode ◽  
Scale Free ◽  
Damage Spreading ◽  
Simplified Algorithm ◽  
Complex Chaotic Systems ◽  
Statistical Effects

We describe systems using Kauffman and similar networks. They are directed functioning networks consisting of finite number of nodes with finite number of discrete states evaluated in synchronous mode of discrete time. In this paper we introduce the notion and phenomenon of "structural tendencies". Along the way we expand Kauffman networks, which were a synonym of Boolean networks, to more than two signal variants and we find a phenomenon during network growth which we interpret as "complexity threshold". For simulation we define a simplified algorithm which allows us to omit the problem of periodic attractors. We estimate that living and human designed systems are chaotic (in Kauffman sense) which can be named — complex. Such systems grow in adaptive evolution. These two simple assumptions lead to certain statistical effects, i.e., structural tendencies observed in classic biology but still not explained and not investigated on theoretical way. For example, terminal modifications or terminal predominance of additions where terminal means: near system outputs. We introduce more than two equally probable variants of signal, therefore our networks generally are not Boolean networks. They grow randomly by additions and removals of nodes imposed on Darwinian elimination. Fitness is defined on external outputs of system. During growth of the system we observe a phase transition to chaos (threshold of complexity) in damage spreading. Above this threshold we identify mechanisms of structural tendencies which we investigate in simulation for a few different networks types, including scale-free BA networks.

On the Dynamics of Scale-Free Boolean Networks

2003 ◽  
pp. 43-49 ◽  
Author(s):  
Roberto Serra ◽  
Marco Villani ◽  
Luca Agostini
Keyword(s):  
Boolean Networks ◽  
Scale Free

Semi-synchronous Activation in Scale-Free Boolean Networks

2007 ◽  
pp. 976-985 ◽  
Author(s):  
Christian Darabos ◽  
Mario Giacobini ◽  
Marco Tomassini
Keyword(s):  
Boolean Networks ◽  
Scale Free

DYNAMICS OF INTERCONNECTED BOOLEAN NETWORKS WITH SCALE-FREE TOPOLOGY

2009 ◽  
Author(s):  
C. DAMIANI ◽  
M. VILLANI ◽  
CH. DARABOS ◽  
M. TOMASSINI
Keyword(s):  
Boolean Networks ◽  
Scale Free
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