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Activity patterns on random scale-free networks: Global dynamics arising from local majority rules | | Haijun Zhou
; Reinhard Lipowsky
; | | Date: |
18 Jan 2007 | | Subject: | Disordered Systems and Neural Networks; Statistical Mechanics | | Abstract: | Activity or spin patterns on random scale-free network are studied by mean field analysis and computer simulations. These activity patterns evolve in time according to local majority-rule dynamics which is implemented using (i) parallel or synchronous updating and (ii) random sequential or asynchronous updating. Our mean-field calculations predict that the relaxation processes of disordered activity patterns become much more efficient as the scaling exponent $gamma$ of the scale-free degree distribution changes from $gamma >5/2$ to $gamma < 5/2$. For $gamma > 5/2$, the corresponding decay times increase as $ln(N)$ with increasing network size $N$ whereas they are independent of $N$ for $gamma < 5/2$. In order to check these mean field predictions, extensive simulations of the pattern dynamics have been performed using two different ensembles of random scale-free networks: (A) multi-networks as generated by the configuration method, which typically leads to many self-connections and multiple edges, and (B) simple-networks without self-connections and multiple edges. | | Source: | arXiv, cond-mat/0701432 | | Services: | Forum | Review | PDF | Favorites | |
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