王新剛Networkgrowthundertheconstraintof王新剛約束下的網(wǎng)絡(luò)增長

Networkgrowthundertheconstraint

ofsynchronizationstabilityXingangWangDepartmentofPhysics,ZJUOct.17,2023,SuzhouNetworkisgrowingExternaldemand:techonologicalandinformationnetworks,etc.DrivingforcesFunctionrequirement:social,economyandbiologynetworks,etc.1.Growth2.PreferentialattachementSmoothgrowth?BAgrowthmodel(SFN)[1][1]R.AlbertandA.-L.Barabasi,Rev.Mod.Phys.74,47(2023).NetworkgrowthinrealworldIntermitentgrowthUnevengrowthEcologicalnetworks[3]Otherexamples:WWW,Internet,authorship,etc.[2]P.HolmeandB.J.Kim,Phys.Rev.E65,066109(2023).[3]J.I.Perotti,et.al.,Phys.Rev.Lett.103.108701(2023).Technologicalnetworks(power-grid)[2]Dynamicgrowth!Outline:Phenomenon

Properties

Mechanisms

ConsequencesThemodelGrowth(BA)Preferentialattachement(BA)Synchronizationstability(functionality)SynchronizableNon-synchronizable[4]A.E.Motter,et.al.,EPL69,334(2023).TheviewpointfromevolutionarynetworkNode

dynamicsGrowth

dynamicsStructureTime-scaleseparationtimeunitfornodeadditioncharacteringtimeforsystemdynamics(synchronization)Nocontraint,BASFNAdiabaticgrowth,constraintactivatedEntangleddynamicsMasterstabilityfunction(MSF)[5][5]M.BarahonaandL.M.Pecora,PRL89,054101(2023).synchronizabilityEigen-spectrumofNecessarycondition:MSFoflogisticmapa=4Aschematicplotonnetworkgrowth[6]A.Arenas,et.al.,Phys.Rep.469,93(2023).?Questions:Acceptingprobability

Wherethenewnodeisconnectedto

ThepropertiesofthegeneratednetworkTheboundaryeigenvaluesParameters:BASFNR=4,ConstrainedBASFNR=4,Constrained(a)(b)Acceptingprobability(missing)MthenumberoftryingadditionsIntermittent,non-smoothgrowthP(M)Wheremissingoccurs?Emergenceofsuper-nodeConsequenceofdynamicgrowthBAR=4R=3.8Super-nodeSFN(SN-SFN)SN-SFNinpracticeInternetatASlevel[7]StockmarketofNewYork[8][7]M.E.J.Newman,SIAMRev.45,167(2023).[8]G.Bonanno,et.al.,Phys.Rev.E68,046130(2023).Super-nodeTopologicalpropertiesofSN-SFNNetworkaveragediameterAveragedclusteringcoefficientAnotherquestiontoBASFN:Ispreferentialattachementanecessarycondition?NetworkgrowthwithrandomattachementMissingdistributionMissinglocationDynamicgrowthstillNetworkgrowthwithrandomattachementDynamicsstabilityPreferentialattachement?SFNwithrandomattachementStar-networkSyn.StabilityVariationofeigen-spectrumFastincreaseSlowincreaseSN-SFNDirectsimulationsLocaldynamicsMissingdistributionSuper-nodeRemarks&discussionsTheuseofsynchronizationconstraint

ThevalueofR

Newviewpointfornetworkevolution

Specificformofgro