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时标上一类BAM神经网络模型的伪概周期解研究.docx

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时标上一类BAM神经网络模型的伪概周期解研究 1.Introduction BAM(BidirectionalAssociativeMemory)neuralnetworkisatypeofrecurrentneuralnetworkthathasbeenwidelyusedinvariousfields,suchaspatternrecognition,imageprocessing,andfaultdiagnosis.TheBAMneuralnetworkmodelhasauniquestructure,whichconsistsoftwointerconnectedlayers,andiscapableoflearningandstoringassociationsbetweenpatterns.However,theBAMneuralnetworkhassomedrawbacks,suchastheproblemofconvergenceandthelackofoscillatorybehavior.Inthispaper,wefocusonthestudyofpseudo-periodicsolutionsinaclassofBAMneuralnetworkmodels,whichcanprovideatheoreticalbasisforfurtherresearchinthisfield. 2.BAMNeuralNetworkModel TheBAMneuralnetworkmodelconsistsoftwolayers,aninputlayer,andanoutputlayer.Theneuronsintheinputlayerreceiveinputpatternsandtheneuronsintheoutputlayerproduceoutputpatterns.Eachneuronintheinputlayerisconnectedtoalltheneuronsintheoutputlayer,andeachneuronintheoutputlayerisconnectedtoalltheneuronsintheinputlayer.TheconnectionsbetweenneuronsarerepresentedbyaweightmatrixW,whichisasymmetricmatrix. ThedynamicsoftheBAMneuralnetworkmodelcanbedescribedbythefollowingequations: x(t+1)=f(a(t)+W*y(t)) y(t+1)=g(b(t)+W*x(t)) wherex(t)andy(t)aretheinputandoutputpatternsattimet,respectively,f(.)andg(.)aretheactivationfunctions,anda(t)andb(t)arethebiasvectors. 3.Pseudo-PeriodicSolutions Pseudo-periodicsolutionsrefertothesolutionsoftheBAMneuralnetworkmodelthatexhibitquasi-periodicoscillationsundercertainconditions.InaclassofBAMneuralnetworkmodels,ithasbeenshownthatwhentheweightmatrixWhasaspecificform,thepseudo-periodicsolutionsexistundercertaininitialconditions. Toobtainthepseudo-periodicsolutions,wefirstassumethattheweightmatrixWcanbedecomposedintotwoparts,adiagonalpartDandanondiagonalpartN,i.e.,W=D+N,whereDisadiagonalmatrixandNisasymmetricmatrixwithzerodiagonals.Then,wedefinetwonewvariablesz(t)andw(t)as: z(t)=x(t)-y(t) w(t)=x(t)+y(t) BysubstitutingtheaboveequationsintotheBAMneuralnetworkmodel,wecanobtainthefollowingequationsforz(t)andw(t): z(t+1)=f(a(t)+(D+N)*w(