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1、BreakingSynchronybyHeterogeneityinComplexNetworksMichaelDenker,MarcTimme,MarkusDiesmann,FredWolf,andTheoGeiselMax-Planck-Institutf¨urStr¨omungsforschungandFakult¨atf¨urPhysik,Universit¨atG¨ottingen,37073G¨ottingen,GermanyFornetworksofpulse-coupledoscillatorswithcomplexconnectivity,wedemon
2、stratethatinthepresenceofcouplingheterogeneitypreciselytimedperiodicfiringpatternsreplacethestateofglobalsynchronythatexistsinhomogenousnetworksonly.Withincreasingdisorder,thesepatternspersistuntiltheyreachacriticaltemporalextentthatisoftheorderoftheinteractiondelay.Forstrongerdisorderthes
3、epatternsceasetoexistandonlyasynchronous,aperiodicstatesareobserved.Wederiveself-consistencyequationstopredicttheprecisetemporalstructureofapatternfromthenetworkheterogeneity.Moreover,weshowhowtodesignheterogenouscouplingarchitecturestocreateanarbitraryprescribedpattern.PACSnumbers:05.45.
4、Xt,89.75.Fb,89.75.Hc,87.10.+eUnderstandinghowthestructureofacomplexnetwork[1]abdeterminesitsdynamicsiscurrentlyinthefocusofresearch0.6inphysics,biologyandtechnology[2].Pulse-coupledos-τ=0.1icillatorsprovideaparadigmaticclassofmodelstodescribeφavarietyofnetworksthatoccurinnature,suchaspopu
5、la-0.5∆φ1tionsoffireflies,pacemakerscellsoftheheart,earthquakes,∆φPhasesorneuralnetworks[3,4].Synchronizationisoneofthemost000.10.2prevalentkindsofcollectivedynamicsinsuchnetworks[5].0.4000.10.200.10.2Recenttheoreticalstudies,whichanalyzeconditionsforthe∆ε∆εexistenceandstabilityofsynchronou
6、sstates,havefocusedonhomogenousnetworkswithsimpletopologies,e.g.globalcd10.2couplings[6]orregularlattices[7].Innature,however,in-tricatelystructuredandheterogenousinteractionsareubiqui-tous.Previously,aspectsofheterogeneityhavebeenstudied0.50.1mostlyingloballycouplednetworks[8,9,10].Howev
7、er,fornetworkswithstructuredconnectivityonlyafewstudiesexistNetworkRateNetworkRate[11,12]anditisstillanopenquestion,howheterogeneityin-0001230123fluencesthedynamics,inparticularsynchronization,insuchTimeTimenetworks.InthisLetterwepresentanexactanalysisofthedynam-FIG.
