1、Effects of External Links on the Synchronization of Community Networks,ZHAO Ming2010.10,Collaborators:,Changsong Zhou周昌松， 香港浸会大学Jinhu Lv吕金虎，中科院数学与系统科学研究员Bambi Hu 胡斑比，香港浸会大学Choi Heng Lai 赖载兴，新加坡国立大学,Outline,Community and inter-linkEffects of external link number on network synchronizationEffects of e
2、xternal link connecting strategy on network synchronizationEffects of external link strength on network synchronizationConclusion,Community and external link,Community: a group of nodes that have denser links among them than with the rest of networkExternal link: links that connect nodes between dif
3、ferent communitiesInternal link: links that connect nodes in the same community,community,internal link,External link,Community Network Model,Individual node:Rossler attractor with bounded synchronization region.,Effects of external link number,Take two random networks as communities and rewire the
4、internal link to the other community, after the first external link emerges, the community network has the largest modularity, with the increasing of rewiring probability, the modularity will decrease by and by. We investigate the synchronization performance of the community network as whole and tha
5、t of the individual community.,Correlation VS. coupling strength,The whole network: larger modularity will decrease the global synchronizability, and when there are few external links, the global synchronizability will not increase monotonically with the coupling strength.Individual community: fewer
6、 external links do not always mean better synchronization performance of community.,Dynamical modularity VS. coupling strength,Definition: the correlation between each pair of nodes at some coupling strength is the strength of dynamical links between the two nodes, which will change with the vary of
7、 coupling strength.,There are two peaks and clearly, larger topological modularity will ensure larger dynamical modularity.,Correlation and dynamical modularity VS. topological modularity,Decrease monotonically,Decrease first and then increase,Increase monotonically,Cat cortical network,53 Nodes, 82
8、6 weighted links, 4 communitiesThe network is rewired to decrease or increase the topological modularity,Correlation VS. topological modularity of Cat cortical network,Dynamical modularity VS. topological modularity of Cat cortical network,Effects of external link connecting strategy,The connecting
9、strategies, such as connecting different communities by randomly selected nodes,by hub nodes,or by connecting hub nodes with randomly selected nodes in the other communities.will affect the synchronization performance.,Sketch map of connecting strategy,Take BA networks as communities and arrange nod
10、es in the same community according to degree, and then connectI: random selected nodesII: nodes selected with probability proportional to k4 III: hub nodes and random selected nodesIV: nodes with larger degree V: nodes with middle degreeVI: nodes with smaller degree between different communities.,II
11、I,IV,V,VI,Correlation VS. coupling strength,I: random selected nodesII: nodes selected with probability proportional to k4 III: hub node and random selected nodesIV: nodes with larger degree V: nodes with middle degreeVI: nodes with smaller degree,Community: no great differences between different st
12、rategies, but with the increasing of external links, strategy VI has the largest average correlationNetwork: when the external links are too few the differences are not prominent, and when there are enough external links, the global synchronization performance will change from better to worse accord
13、ing to the sequence IVIIIIIVVII.,Dynamical modularity VS. coupling strength,Effects of external link strength I,The strength of internal links is kept 1, and the strength of external links changes from 0.5 to 3.,Effects of external link strength II,Conclusion of this work,External links can increase
14、 the global network synchronizability, but they also decrease the synchronization performance of individual community in some modularity region;Connecting hub nodes does not guarantee better global network synchronizability;Stronger strength of external links will enhance global network synchronizability, but narrow down the coupling strength region.,Thank you！,
