王青云-生物神經(jīng)元網(wǎng)絡(luò)動力學(xué)的研究進展課件

SomeRecentStudyinBiologicalNeuronalOscillatoryNetworks

QingyunWang(王青云)DepartmentofDynamicsandControl,BeihangUniversity,Beijing100191Email:qingyunwang@7/29/20231WithcomplimentsProf.LuQishao(BeihangUniversity)Prof.Duan

ZhiSheng(PekingUniversity)Prof.ChenGuanRong(CityUniversityofHongKong)Dr.Matjaz

Perc(UniversityofMaribor,Koroska

cesta160,SI-2000Maribor,Slovenia)7/29/20232ContentsMotivationNeuronalstructureandnetworkDynamicsofasingleneuronSynchronizationtransitionandRhythmdynamicsonnetworksBurstingDynamicsonRealisticNeuronalNetworksSpatialResonanceinNeuronalNetworksOpenproblems

7/29/20233Thesingleneuroninthevertebratecortexconnectstomorethan10,000postsynapticneuronsviasynapsesformingcomplexnetworks.Thebiologicalnervoussystemcancommunicateandtransforminformationthroughinteractionofnetworks.Neuronalinformationencodingandprocessingarereflectedbyoscillationpatternsofelectricalimpulsesequencesinneurons.Motivation7/29/20234Neurodynamicsdealswiththedynamicsandcontrolproblemsofelectricalactivitiesandinformationprocessesinnervoussystemsandisimportantintheresearchofbiologicalmotionsandintelligentbehavior.Neurodynamicsisamulti-disciplinaryresearchareainnonlineardynamics,networkscienceandneuroscience.Synchronizationisofgreatimportanceforsignalencodingandtransductionininformationprocessingofneuronsintworespects.Biologicalneuronscanextractthehinderedinformationbystochasticresonance.7/29/202356

NeuralMedicineandEngineering

NeuronalfiringandinformationencodingBiologicalControlBiologicalcomplexneuronalnetworksIntelligentRobotsBiologicalstructureofnervoussystemsNeuralCognitiveScienceNeuralComputersNeuralMedicalTechniques7/29/20236StructureofSingleNeuron

Abasic

elementforinformationprocessinginnervoussystems.Thereareabout1011

neuronsinthehumanbrainand104synapsesforaneuron.7/29/20237Modelofneuron

(1)

(4)(3)(2)

HodgkinA.L.,HuxleyA.F.,J.physiol.(London),1952,(117)500-544Hodgkin-Huxleymodel(1952NobelPrize)Chaymodel,HRmodel,FHNmodel,Rulkovmapetc.NonlinearODEsinvolvingmultipletimescales.

Hardtoanalyzebothmathematicallyandcomputationally.7/29/20238Diversityoffiringpatternsofasingleneuron

(inexperimentalneuralpacemakers)

(LiLi,RenWei,2003,2004)

7/29/20239Bifurcationscenario

(intheoreticalmodelandexperimentalneuralpacemakers)

(LiLi,RenWeietal,IJBC,2004.DuanLiXiaetal,Neurocomputing2008)

Chaymodel7/29/202310Chaos(inexperimentalneuralpacemakers)

betweenperiod2andperiod3firings(RenWei,IJBC,1997)

7/29/2023117/29/202312NeuronalnetworksWhatisaBrain?densenetworkmorethan104cellbodiesandseveralkilometersof`wires'percubicmillimeter.Manytypesofcells:spikingneurons(1011cells),gliacells(`supporter'cellsnotinvolvedintheinformationprocessing)andanalogneurons.7/29/202313Synapseanddelay7/29/202314Dorsalandlateralviewsoftheconnectivitybackboneofhumanbrain.Labelsindicatinganatomicalsubregionsareplacedattheirrespectivecentersofmass.Nodes(individualROIs)arecodedaccordingtostrengthandedgesarecodedaccordingtoconnectionweight.HagmannP,CammounL,GigandetX,MeuliR,HoneyCJ,WedeenVJ,SpornsO(2008)Mappingthestructuralcoreofhumancerebralcortex.PLoSBiologyVol.6,No.7,e1597/29/202315NeuronalnetworksNeuronalnetworksinvolvealargenumberofindividualneurons.Detailsoftheconnectivitynotusuallyknown.HardtoanalyzehowconnectivityinfluencesODEdynamics.7/29/202316NeuronalsynchronizationSynchronizationseemstobeverycrucialfortheefficientprocessingandtransmissionofinformationacrossthenervesystem.Parkinson'stremorisrelatedtoneuronalsynchronization.Transientlysynchronizedassembliesofneuronsarebelievedtounderliecognitivefunctions.Thereisconsistentevidenceforareductionofsynchronizationinschizophrenia.7/29/202317RobertC.Elsonetal,Phys.ReviewLett

815692-56951998TwocoupledneuroncircuitSynchronizedmotions7/29/202318Hua

GuangGUetal,CHIN.PHYS.LETT.Vol.26,No.11(2009)110501Experimentresults7/29/202319PNAS2010Listener-speakercanvalidlycommunicationbymeansofneuronalcoupling7/29/202320Classificationofsynchronization7/29/202321Burstsynchronizationanddesynchronizationin\fold/homoclinic"(\square-wave")bursters.ShownaresimulationsofcoupledMorris-Lecarsystemswithadditionalslowvariables.Variousregimesofsynchronizationofbursters(modiedfrom[Izhikevich,2000a]).7/29/202322Singularphaselocking7/29/202323AnalysismethodofphaselockingSingularperturbationtheory(Terman

etal,JComput

Neurosci(2007)23:217–235)Dynamicclusteringinthe(a)fulland(b)reducedmodels.TherearetwentypairsofE-andI-cells.EachE-cellexcitesoneI-cellandeachI-cellinhibitsthreeE-cellsLimited:Networkstructure,connectionstyle7/29/202324Phaseresponsecurve(discretemapmethod)CarmenCanavier7/29/202325Therearestillmanyothermethods:

Hilberttransformationoftimeseries,Poincaremapmethod(numericalcomputation)7/29/202326IncorporatingnoiseanddelayNoiseinduced(enhanced)synchronization.(twocoupledneuronsandlargescaleneuronalnetworks)Noiseinducedspatiotemporalwavepatterns(targetwave,spiralwave(Majun),spatialcoherence)Delayinducedcomplexityinneuronalnetworks(varioussynchronizationtransitionandspatialcoherence)7/29/202327EffectofdelayontwocoupledneuronsQYWangetal,IJBC,18,4(2008)1189–11987/29/202328EffectofdelayonlargescaleneuronalnetworksDynamicsmodel7/29/202329Zig-zagfrontsAntiphaseclusteringsunhcronizationInphasesynchronizationagain7/29/202330Measure:Q.Y.Wang,Z.SDuan,M.Perc,G.R.Chen,EPL,83(2008)500087/29/202331(Continued)A.-L.BarabásiandR.Albert,Science286,50919997/29/202332Increasingdelay7/29/2023337/29/2023347/29/2023357/29/2023367/29/202337QingyunWang,

Matjaz

Perc,Zhi

Sheng

Duan,GuanRongChen,PhysicalReviewE,80,026206,2009.7/29/202338Attractivecoupling7/29/202339Repulsivecoupling7/29/202340Burstingperiod

7/29/202341BurstingsynchronizationMacaquecorticalnetwork,consistingof95nodesand2402links7/29/202342Mathematicalmodel7/29/202343BurstingsynchronizationSpace-timeplotsofx(t)asobtainedforD=2.0andI_{ext}=3.2withdifferentinformationtransmissiondelays\tau,equalling:(a)0,(b)7,(c)14,(d)22,(e)30.Noticetheburstingsynchronizationandspikesinburstincreaseas\tauincreases.LiangXiaoMingetal,2009PRE7/29/202344Inordertoquantitativelydescribeglobalnetworkstates,we

definethequantitymThemoresynchronoustheneuronalnetworkis,thelargeristheparameterm.Further,itcanalsoidentifytransitionofdifferentbursts.Thus,itiscalledburstsynchronizationtransitionparameter.7/29/202345Dependenceoftheburstsynchronizationparametermon$\tau$fordifferentvaluesofdiffusionD7/29/202346Dependenceoftheburstsynchronizationparametermon$\tau$fordifferentvaluesoftheexternalstimulusI7/29/202347

Resonance

ResonanceofasingleHHneuron7/29/202348Resonance7/29/202349Spatialresonanceofnetworks7/29/202350SpatialcoherenceresonanceModelSet-UpHodgkinandHuxleymodelTransmissiondelaynoisetheEulerMaruyamamethod7/29/202351EffectofdelayAsthenoiseincreases,patternisdestroyed.

Thereisanintermediatenoise,circularpatterncanappear.7/29/202352Spatialstructurefunction:Circularaverage:Signal-noise-ratio:TwodimensionalFourierTransform7/29/202353Spatialstructurefunction

7/29/202354CircularaverageandSNRMaximumindicatingcoherence7/29/202355Fordifferentdelays,dependenceofSNRonnoise.7/29/202356EffectofsmallworldconnectionAsqisincreased,Snrdecreases.7/29/202357OpenproblemsDynamicalmechanismofsynchronizationbifurcation:synchronization-antiphasesynchronization---synchronizationasthedelay/linkprobabilityisvariedonsmallworld/scalefreenetworks.Dynamicalbifurcationmechanismofburstingfiringshouldbeexploredasthedelayisincreased.Theoryexplorationofsingularphaselocking.Dynamicsofmorerealisticneuronalnetworks7/29/202358Q.Y.Wang,Z.S.Duan,L.Huang,G.R.Chen,Q.S.Lu,Patternformationandfiringsynchronizationinnetworksofmapneurons,NewJournalofPhysics,9(383):1-11,2007.Q.Y.Wang,Z.S.Duan,Z.S.Feng,G.R.ChenandQ.S.Lu，SynchronizationtransitioninGap-Junction-Coupledleechneurons,PhysicaA,2008,3874404-4410.Q.Y.Wang,Matja?

Perc,Zhisheng

D