一类含时滞的扩散单神经元模型的分岔分析（英文）.docx

一类含时滞的扩散单神经元模型的分岔分析（英文）
Title:BifurcationAnalysisofaClassofTime-DelayedDiffusionSingleNeuronModels
Abstract:
Thestudyofneuraldynamicswithtimedelayshasgainedsignificantattentionduetoitsrelevanceinunderstandingcomplexneuronalbehaviors.Thispaperfocusesonanalyzingthebifurcationphenomenainaclassoftime-delayeddiffusionsingleneuronmodels.Byconsideringtheimpactofthetimedelayonthestabilityanddynamicsofthesystem,weaimtoshedlightontheroleoftimedelaysinneuraldynamicsandprovideinsightsintopotentialbifurcationscenarios.
Introduction:
Neuronsareknownfortheirabilitytotransmitandprocessinformationthroughcomplexelectricalandchemicalsignaling.Modelingneuronalbehavioriscrucialforunderstandingvariousneurologicalphenomenaanddesigningeffectivetherapeuticstrategies.Theinclusionoftimedelaysinneuralmodelsisimportantbecausedelaysinsignalpropagationcansignificantlyimpactthedynamicsandstabilityofneurons.
Thediffusionequationprovidesamathematicalframeworkformodelingthespreadofsubstancesorinformationinspace.Combiningdiffusionwithsingleneuronmodelsallowsustostudyhowinformationspreadsthroughneuralnetworks.However,theintroductionoftimedelaysaddsanadditionallayerofcomplexitytothesemodels.
Methods:
Toanalyzethebifurcationphenomenaintime-delayeddiffusionsingleneuronmodels,weutilizetechniquesfromdynamicalsystemstheory.Specifically,weconsiderbothlocalandglobalstabilityanalysis,aswellasnumericalsimulationstoillustratevariousbifurcationscenarios.
Results:
Ouranalysisrevealsthattheinclusionoftimedelaysindiffusionsingleneuronmodelscanleadtorichbifurcationbehavior.Bysystematicallyvaryingthevaluesofneuronalparameters,suchasthediffusioncoefficient,timedelay,andfiringthreshold,weobservevariousbifurcationscenarios,includingHopfbifurcations,saddle-nodebifurcations,andperiod-doublingbifurcations.Thesebifurcationphenomenaindicatetheemergenceofcomplexoscillatorydynamicsandmultiplestablestatesintheneuronmodel.
Discussion:
Thefindingsofthisstudyhighlighttheimportanceofconsideringtimedelaysinthemodelingofneuronaldynamic