复杂网络上动力系统同步的研究进展课件

EffectsofExternalLinksontheSynchronizationofCommunityNetworksZHAOMing2010.10EffectsofExternalLinksont1Collaborators:ChangsongZhou周昌松，香港浸会大学JinhuLv吕金虎，中科院数学与系统科学研究员BambiHu胡斑比，香港浸会大学ChoiHengLai赖载兴，新加坡国立大学Collaborators:ChangsongZhou周昌2OutlineCommunityandinter-linkEffectsofexternallinknumberonnetworksynchronizationEffectsofexternallinkconnectingstrategyonnetworksynchronizationEffectsofexternallinkstrengthonnetworksynchronizationConclusionOutlineCommunityandinter-lin3CommunityandexternallinkCommunity:agroupofnodesthathavedenserlinksamongthemthanwiththerestofnetworkExternallink:linksthatconnectnodesbetweendifferentcommunitiesInternallink:linksthatconnectnodesinthesamecommunitycommunityinternallinkExternallinkCommunityandexternallinkCom4CommunityNetworkModelIndividualnode:Rosslerattractorwithboundedsynchronizationregion.CommunityNetworkModelIndivid5EffectsofexternallinknumberTaketworandomnetworksascommunitiesandrewiretheinternallinktotheothercommunity,afterthefirstexternallinkemerges,thecommunitynetworkhasthelargestmodularity,withtheincreasingofrewiringprobability,themodularitywilldecreasebyandby.Weinvestigatethesynchronizationperformanceofthecommunitynetworkaswholeandthatoftheindividualcommunity.Effectsofexternallinknumbe6CorrelationVS.couplingstrengthThewholenetwork:largermodularitywilldecreasetheglobalsynchronizability,andwhentherearefewexternallinks,theglobalsynchronizabilitywillnotincreasemonotonicallywiththecouplingstrength.Individualcommunity:fewerexternallinksdonotalwaysmeanbettersynchronizationperformanceofcommunity.CorrelationVS.couplingstren7DynamicalmodularityVS.couplingstrengthDefinition:

thecorrelationbetweeneachpairofnodesatsomecouplingstrengthisthestrengthofdynamicallinksbetweenthetwonodes,whichwillchangewiththevaryofcouplingstrength.Therearetwopeaksandclearly,largertopologicalmodularitywillensurelargerdynamicalmodularity.DynamicalmodularityVS.coupl8CorrelationanddynamicalmodularityVS.topologicalmodularityDecreasemonotonicallyDecreasefirstandthenincreaseIncreasemonotonicallyCorrelationanddynamicalmodu9Catcorticalnetwork53Nodes,826weightedlinks,4communitiesThenetworkisrewiredtodecreaseorincreasethetopologicalmodularityCatcorticalnetwork53Nodes,10CorrelationVS.topologicalmodularityofCatcorticalnetworkCorrelationVS.topologicalmo11DynamicalmodularityVS.topologicalmodularityofCatcorticalnetworkDynamicalmodularityVS.topol12EffectsofexternallinkconnectingstrategyTheconnectingstrategies,suchasconnectingdifferentcommunitiesbyrandomlyselectednodes,byhubnodes,orbyconnectinghubnodeswithrandomlyselectednodesintheothercommunities.willaffectthesynchronizationperformance.Effectsofexternallinkconne13SketchmapofconnectingstrategyTakeBAnetworksascommunitiesandarrangenodesinthesamecommunityaccordingtodegree,andthenconnectI:randomselectednodesII:nodesselectedwithprobabilityproportionaltok^4III:hubnodesandrandomselectednodesIV:nodeswithlargerdegreeV:nodeswithmiddledegreeVI:nodeswithsmallerdegreebetweendifferentcommunities.IIIIVVVISketchmapofconnectingstrat14CorrelationVS.couplingstrengthI:randomselectednodesII:nodesselectedwithprobabilityproportionaltok^4III:hubnodeandrandomselectednodesIV:nodeswithlargerdegreeV:nodeswithmiddledegreeVI:nodeswithsmallerdegreeCommunity:nogreatdifferencesbetweendifferentstrategies,butwiththeincreasingofexternallinks,strategyVIhasthelargestaveragecorrelationNetwork:whentheexternallinksaretoofewthedifferencesarenotprominent,andwhenthereareenoughexternallinks,theglobalsynchronizationperformancewillchangefrombettertoworseaccordingtothesequenceI>VI>III>IV>V>II.CorrelationVS.couplingstren15DynamicalmodularityVS.couplingstrengthDynamicalmodularityVS.coupl16EffectsofexternallinkstrengthI

Thestrengthofinternallinksiskept1,andthestrengthofexternallinkschangesfrom0.5to3.Effectsofexternallinkstren17EffectsofexternallinkstrengthIIEffectsofexternallinkstren18ConclusionofthisworkExternallinkscanincreasetheglobalnetworksynchronizability,buttheyalsodecreasethesynchronizationperformanceofindividualcommunityinsomemodularityregion;Connectinghubnodesdoesnotguaranteebetterglobalnetworksynchronizability;Strongerstrengthofexternallinkswillenhanceglobalnetworksynchronizability,butnarrowdownthecouplingstrengthregion.ConclusionofthisworkExterna19Thankyou！Thankyou！20EffectsofExternalLinksontheSynchronizationofCommunityNetworksZHAOMing2010.10EffectsofExternalLinksont21Collaborators:ChangsongZhou周昌松，香港浸会大学JinhuLv吕金虎，中科院数学与系统科学研究员BambiHu胡斑比，香港浸会大学ChoiHengLai赖载兴，新加坡国立大学Collaborators:ChangsongZhou周昌22OutlineCommunityandinter-linkEffectsofexternallinknumberonnetworksynchronizationEffectsofexternallinkconnectingstrategyonnetworksynchronizationEffectsofexternallinkstrengthonnetworksynchronizationConclusionOutlineCommunityandinter-lin23CommunityandexternallinkCommunity:agroupofnodesthathavedenserlinksamongthemthanwiththerestofnetworkExternallink:linksthatconnectnodesbetweendifferentcommunitiesInternallink:linksthatconnectnodesinthesamecommunitycommunityinternallinkExternallinkCommunityandexternallinkCom24CommunityNetworkModelIndividualnode:Rosslerattractorwithboundedsynchronizationregion.CommunityNetworkModelIndivid25EffectsofexternallinknumberTaketworandomnetworksascommunitiesandrewiretheinternallinktotheothercommunity,afterthefirstexternallinkemerges,thecommunitynetworkhasthelargestmodularity,withtheincreasingofrewiringprobability,themodularitywilldecreasebyandby.Weinvestigatethesynchronizationperformanceofthecommunitynetworkaswholeandthatoftheindividualcommunity.Effectsofexternallinknumbe26CorrelationVS.couplingstrengthThewholenetwork:largermodularitywilldecreasetheglobalsynchronizability,andwhentherearefewexternallinks,theglobalsynchronizabilitywillnotincreasemonotonicallywiththecouplingstrength.Individualcommunity:fewerexternallinksdonotalwaysmeanbettersynchronizationperformanceofcommunity.CorrelationVS.couplingstren27DynamicalmodularityVS.couplingstrengthDefinition:

thecorrelationbetweeneachpairofnodesatsomecouplingstrengthisthestrengthofdynamicallinksbetweenthetwonodes,whichwillchangewiththevaryofcouplingstrength.Therearetwopeaksandclearly,largertopologicalmodularitywillensurelargerdynamicalmodularity.DynamicalmodularityVS.coupl28CorrelationanddynamicalmodularityVS.topologicalmodularityDecreasemonotonicallyDecreasefirstandthenincreaseIncreasemonotonicallyCorrelationanddynamicalmodu29Catcorticalnetwork53Nodes,826weightedlinks,4communitiesThenetworkisrewiredtodecreaseorincreasethetopologicalmodularityCatcorticalnetwork53Nodes,30CorrelationVS.topologicalmodularityofCatcorticalnetworkCorrelationVS.topologicalmo31DynamicalmodularityVS.topologicalmodularityofCatcorticalnetworkDynamicalmodularityVS.topol32EffectsofexternallinkconnectingstrategyTheconnectingstrategies,suchasconnectingdifferentcommunitiesbyrandomlyselectednodes,byhubnodes,orbyconnectinghubnodeswithrandomlyselectednodesintheothercommunities.willaffectthesynchronizationperformance.Effectsofexternallinkconne33SketchmapofconnectingstrategyTakeBAnetworksascommunitiesandarrangenodesinthesamecommunityaccordingtodegree,andthenconnectI:randomselectednodesII:nodesselectedwithprobabilityproportionaltok^4III:hubnodesandrandomselectednodesIV:nodeswithlargerdegreeV:nodeswithmiddledegreeVI:nodeswithsmallerdegreebetweendifferentcommunities.IIIIVVVISketchmapofconnectingstrat34CorrelationVS.couplingstrengthI:randomselectednodesII:nodesselectedwithprobabilityproportionaltok^4III:hubnodeandrandomselectednodesIV:nodeswithlargerdegreeV:nodeswithmiddledegreeVI:nodeswithsmallerdegreeCommunity:nogreatdifferencesbetweendifferentstrategies,butwiththeincreasingofexternallinks,strategyVIhasthelargestaveragecorrelationNetwork:whentheexternallinksaretoofewthedifference