復雜網(wǎng)絡上動力系統(tǒng)同步的研究進展

1、Effects of External Links on the Synchronization of Community Networks,ZHAO Ming2010.10,Collaborators:,Changsong Zhou周昌松， 香港浸會大學Jinhu Lv呂金虎，中科院數(shù)學與系統(tǒng)科學研究員Bambi Hu 胡斑比，香港浸會大學Choi Heng Lai 賴載興，新加坡國立大學,Outline,Communi

2、ty and inter-linkEffects of external link number on network synchronizationEffects of external link connecting strategy on network synchronizationEffects of external link strength on network synchronizationConclusion

3、,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 different communitiesInternal link: links that con

4、nect 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

5、networks as communities and rewire the 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 modul

6、arity will decrease by and by. We investigate the synchronization performance of the community network as whole and that of the individual community.,Correlation VS. coupling strength,The whole network: larger modul

7、arity 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 external links

8、 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 dynamica

9、l links between the two nodes, which will change with the vary of coupling strength.,,There are two peaks and clearly, larger topological modularity will ensure larger dynamical modularity.,Correlation and dynamical modu

10、larity VS. topological modularity,,Decrease monotonically,Decrease first and then increase,Increase monotonically,Cat cortical network,53 Nodes, 826 weighted links, 4 communitiesThe network is rewired to decrease or inc

11、rease 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 con

12、necting 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 p

13、erformance.,Sketch map of connecting strategy,Take BA networks as communities and arrange nodes in the same community according to degree, and then connectI: random selected nodesII: nodes selected with probability pro

14、portional to k^4 III: hub nodes and random selected nodesIV: nodes with larger degree V: nodes with middle degreeVI: nodes with smaller degree between different communities.,III,IV,V,VI,Correlation VS. couplin

15、g strength,I: random selected nodesII: nodes selected with probability proportional to k^4 III: hub node and random selected nodesIV: nodes with larger degree V: nodes with middle degreeVI: nodes with smaller de

16、gree,Community: no great differences between different strategies, but with the increasing of external links, strategy VI has the largest average correlationNetwork: when the external links are too few the differences a

17、re not prominent, and when there are enough external links, the global synchronization performance will change from better to worse according to the sequence I>VI>III>IV>V>II.,Dynamical modularity VS. coup

18、ling 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

19、links can increase 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 net