幾類環(huán)狀三元神經(jīng)網(wǎng)絡系統(tǒng)的動力學分析.pdf

1、湖南大學碩士學位論文幾類環(huán)狀三元神經(jīng)網(wǎng)絡系統(tǒng)的動力學分析姓名：曹棟申請學位級別：碩士專業(yè)：應用數(shù)學指導教師：黃立宏20060418碩士學位論文AbstractThenetworkwitharingofthreeidenticalneuronshassignificantbiologicalandphysicalbackgroundsandmanymodelsofneuralnetworkshavebeenproposedasthissp

2、ecialcaseThisthesisdealswithseveralclassessystemsofnetworkswhichhasdiscontinuousmessagefunctionWeobtaintheconvergenceofthesystemundersomecertainparameterconditionsFirst，wedeaiwithanetworkwitharingofthreeidenticalneuronsw

3、hichhasdiscontinuousmessagefunctionWeobtaintheconvergenceofthesystemtoequilibriumswithsomecertainparameterconditionsTogoonwithweconsideraclassofdelaydifferentialsystemswhichdescribingtheevolutionofnetworkwitharingofthree

4、identicalneuronsByapplyingitssymmetrythetheoryofdifferentialdifferenceequationandstudyingitslimitingequation，ouranalysisshowstheconvergenceofthesystemwhenthethresholdisnotlessthani1Finallythereisaclassofnetworkwitharingo

5、fthreeidenticalneuronswhichhasadisproportionmessagefunctionWehavesomespecialstudyoftheabovesystemwiththelimitthatthethresholdislargerthanj1Wecometotheconclusionthatithasabundantfeatures：whenwerestrictinitialvaluestothegi

6、venphasespace，itssolutionmaybecolwergenttosomestablepoints，butothersmaybeconvergenttolimitcycleFromtheanalysisofthemodelsabove，wecancometotheconclusionthattimedelayandmessagefunctionplayvitalrolesinthedynamicalfeaturesof

7、theneuralnetworksThereisnotimedelayinthefirstmodel，andwefindthatithasverysimpledynamicfeaturesWithtimedelaythesecondmodelnotonlyhasconvergencesolution，butalsohasmorestablepointsundersomespecialthresholdvaluesBecauseofthe

8、timedelayanddisproportionmessagefunction，limitcyclesexistinthethirdmodelWiththesamereasonitmakesthethirdmodelthemostsuitableonetetiecttherealworldKeyWords：Differentialequation；Neuralnetwork；Timedelay；Stability；Existence；