scholarly journals Mean-field and non-mean-field behaviors in scale-free networks with random Boolean dynamics

2010 ◽  
Vol 43 (22) ◽  
pp. 225101 ◽  
Author(s):  
A Castro e Silva ◽  
J Kamphorst Leal da Silva
2014 ◽  
Vol 989-994 ◽  
pp. 4524-4527
Author(s):  
Tao Li ◽  
Yuan Mei Wang ◽  
You Ping Yang

A modified spreading dynamic model with feedback-mechanism based on scale-free networks is presented in this study. Using the mean field theory, the spreading dynamics of the model is analyzed. The spreading threshold and equilibriums are derived. The relationship between the spreading threshold, the epidemic steady-state and the feedback-mechanism is analyzed in detail. Theoretical results indicate the feedback-mechanism can increase the spreading threshold, resulting in effectively controlling the epidemic spreading.


2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Satoru Morita

Abstract Spreading phenomena are ubiquitous in nature and society. For example, disease and information spread over underlying social and information networks. It is well known that there is no threshold for spreading models on scale-free networks; this suggests that spread can occur on such networks, regardless of how low the contact rate may be. In this paper, I consider six models with different contact and propagation mechanisms, which include models studied so far, but are apt to be confused. To compare these six models, I analyze them by degree-based mean-field theory. I find that the result depends on the details of contact and propagation mechanism.


2012 ◽  
Vol 562-564 ◽  
pp. 1386-1389
Author(s):  
Yuan Mei Wang ◽  
Tao Li

In the SIR model once a node is cured after infection it becomes permanently immune,but we assume this immunity to be temporary. So we obtain an epidemic model with time delay on scale-free networks. Using the mean field theory the spreading threshold and the spreading dynamics is analyzed. Theoretical results indicate that the threshold is significantly dependent on the topology of scale-free networks and time delay. Numerical simulations confirmed the theoretical results.


2005 ◽  
Vol DMTCS Proceedings vol. AE,... (Proceedings) ◽  
Author(s):  
Zoran Nikoloski ◽  
Narsingh Deo ◽  
Ludek Kucera

International audience Barabási and Albert [1] suggested modeling scale-free networks by the following random graph process: one node is added at a time and is connected to an earlier node chosen with probability proportional to its degree. A recent empirical study of Newman [5] demonstrates existence of degree-correlation between degrees of adjacent nodes in real-world networks. Here we define the \textitdegree correlation―-correlation of the degrees in a pair of adjacent nodes―-for a random graph process. We determine asymptotically the joint probability distribution for node-degrees, $d$ and $d'$, of adjacent nodes for every $0≤d≤ d'≤n^1 / 5$, and use this result to show that the model of Barabási and Albert does not generate degree-correlation. Our theorem confirms the result in [KR01], obtained by using the mean-field heuristic approach.


2013 ◽  
Vol 378 ◽  
pp. 655-661
Author(s):  
Tao Li ◽  
Yuan Mei Wang

Taking into account the heterogeneity of the underlying networks, an epidemic model with feedback-mechanism, time delay and migrations of individuals on scale-free networks is presented. First, the epidemic dynamics is analyzed via the mean field theory. The spreading critical threshold and equilibriums are derived. The existence of endemic equilibrium is determined by the spreading threshold. Then, the influences of feedback-mechanism, time delay, migrations of individuals and the heterogeneity of the scale-free networks on the spreading threshold and the epidemic steady-state are studied in detail. Numerical simulations are presented to illustrate the results with the theoretical analysis.


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