两类时滞细胞神经网络模型的指数稳定性的开题报告Title:ExponentialStabilityofTwoTypesofDelayedCellNeuralNetworkModelsIntroduction:Cellularneuralnetworks(CNNs)havebeenextensivelystudiedduetotheirwiderangeofapplicationsinmanyfieldssuchaspatternrecognition,signalprocessing,andimageprocessing.CNNshavebeenshowntohavesignificantadvantagesovertraditionalmethodsduetotheirparallelprocessingandbiologicalinspiration.However,thepresenceoftimedelayscansignificantlyaffectthestabilityandbehaviorofthesenetworks.Inthisreport,wewillstudytheexponentialstabilityoftwotypesofdelayedCNNmodels.Objectives:Themainobjectiveofthisreportistoinvestigatetheexponentialstabilityoftwotypesofdelayedcellneuralnetworkmodels.Specifically,wewillexamineatypeofCNNmodelwithtime-varyingdelaysandanothertypewithconstantdelays.Weaimtoderiveanalyticalconditionsfortheexponentialstabilityofbothmodelsandvalidateourresultsusingnumericalsimulations.Methodology:WewilluseLyapunovstabilityanalysistoderiveasetofsufficientconditionsfortheexponentialstabilityofthetwotypesofdelayedCNNmodels.Wewillbeginbydefiningthemodelequationsforbothnetworksandintroducingthetimedelays.Next,wewillderivetheLyapunovfunctionanditstimederivativetoobtainthestabilityconditions.Wewillthenvalidateourstabilityconditionsusingnumericalsimulations.ExpectedResults:Weexpecttoderiveanalyticalconditionsfortheexponentialstabilityofbothtypesofdelayedcellneuralnetworkmodels.Weanticipatethatourconditionswillbeexpressedintermsofthenetworkparameterssuchastheconnectionweights,timedelays,andactivationfunctions.Usingnumericalsimulations,wewillvalidateourstabilityconditionsandcompareourresultswithexistingliterature.Conclusion:Inthisreport,weproposedtoinvestigatetheexponentialstabilityoftwotypesofdelayedcellneuralnetworkmodels.OurstudyisimportantasitprovidesabetterunderstandingofthebehaviorandstabilityofCNNsinthepresenceofdelays.TheresultsofourstudycanbeusedtodesignandoptimizeCNNsforvariousapplications.