An event-driven framework for the simulation of networks of(3)

Abstract. We propose an event-driven framework dedicated to the design and the simulation of networks of spiking neurons. It consists of an abstract model of spiking neurons and an efficient event-driven simulation engine so as to achieve good performance

scheduledinstep3)oftheabove-mentionedalgorithm,permitsthecompletionofstep1).siorriwillthenbeusedtocompletethesecondstep.

2.2Connectivity

Theabstractmodeldescribedinthe

previoussectionisimplicitelybasedontheassumptionthattheconnec-

tivityofthespikingneuralnetworkstobesimulatedisofaveryclassi-

caltype:thereexistsa( xed)setoforientedconnectionsbetweentheneurons,andaneuronhasonlyoneFigure1outputchannel(oneaxon)suchthat

aspikeemittedbyaneuronwillalwaysbetransmittedtoallitssuccessors(alltheneuronslinkedtoitsaxon).Thelatterassumptionexplainswhythefunctionsidoesnotprovideanyexplicitwayoftargetingparticularneurons.

Suchaconnectivitypermitsthatthestep3)oftheevent-drivensimulationalgorithm(receptioneventsscheduling)isperformedinacentralizedwaybythesimulationengine,asitonlyrequirestheknowledgeofthelistofsuccessorsforeachneuron.Indeed,itispossiblethatmorethanoneconnectionexistsbetweenapairofneurons(e.g.withdi erenttimedelays),soasingleneuroncanappearmorethanonceinthesuccessorlist.Then,at ringtime,thesimulationenginewillscheduleexactlyoneeventpersynapseinthesuccessorlist.Moreover,inorderforareceiverneurontoreacttoanincomingspike,itwillhavetoknowwhichsynapseisconcerned,whichrequiresthatallsynapsesbeidenti edinthesuccessorlist.Thesynapseidentitycorrespondstothesparameteroftherifunctiongivenintheprevioussection.

Figure1(left)showsasamplenetworkconnectivity,with3neurons(A,B,C)withthesynapseidentitiesexpressedasa1,..,c2,c3.Ontheright,thecorre-spondingsuccessorlistforeachneuronisrepresented.

2.3Relationtoothermodels

Letusnowconsideraleakyintegrate-and- reneuroni,whosemembranepo-tentialViobeysthefollowingequation

dVi= Vi+Iidt(1)

whereIicorrespondstoaconstantinputcurrent.Theneuronisfurtherde nedbyathresholdmechanism,i.e.itwill rewheneverVi>θianditspotentialwillbesettozero(Vi=0)at ringtimes.Forthesakeofsimplicity,weconsiderthatIi>θiinthefollowing.Wefurtherassumeinthefollowingthatwhenevertheneuronireceivesaspikethroughasynapses,attimetr,themembranepotentialVi(tr)instantaneouslyjumpsofanamplitudews.