单个非线性振荡神经元或人工非线性神经网络对输入信号的结构变换(IJISA-V11-N8-1)

I.J.IntelligentSystemsandApplications,2019,8,1-10PublishedOnlineAugust2019inMECS()DOI:10.5815/ijisa.2019.08.01Copyright©2019MECSI.J.IntelligentSystemsandApplications,2019,8,1-10StructuralTransformationsofIncomingSignalbyaSingleNonlinearOscillatoryNeuronorbyanArtificialNonlinearNeuralNetworkRomanPeleshchakUniversityofInformationTechnologyandManagement,Rzeszow,35-225,PolandE-mail:[e-mail]ofInformationSystemsandNetworks,LvivPolytechnicNationalUniversity,Lviv,79012,UkraineE-mail:[e-mail]fMathematics,UniversityofColorado,ColoradoSprings,80918,USAE-mail:[e-mail]entofInformationSystemsandNetworks,LvivPolytechnicNationalUniversity,Lviv,79012,UkraineE-mail:[e-mail]:02February2019;Accepted:20March2019;Published:08August2019Abstract—Structuraltransformationsofincominginformationalsignalbyasinglenonlinearoscillatoryneuronoranartificialnonlinearneuralnetworkareinvestigated.TheneuronsaremodeledasthresholddevicessothattheartificialnonlinearneuralnetworkunderconsiderationaresystemsofnonlinearvanderPoltypeoscillatoryneurons.Theneuronsarecoupledbysynapticweightcoefficientstoendowthesystemswiththeconfigurationtopologyofachainoraring.Itisshownthatthemorphologyoftheoutgoingsignal–withrespecttotheshape,amplitudeandtimedependenceoftheinstantaneousfrequencyofthesignal–attheoutputofsuchaneuralnetworkhasahigherdegreeofstochasticitythanthemorphologyofthesignalattheoutputofasingleneuron.Weconcludethattheprocessofcodingbyasingleneuronoranentirechain-likeorcircularneuralnetworkmaybeconsideredintermsoffrequencymodulations,whichareknowninPhysicsasawaytotransmitinformation.Weconjecturethatfrequencymodulationsconstituteoneofthewaysofcodingofinformationbytheneuronsinthesetypesofneuralnetworks.IndexTerms—Nonlinearneuron,artificialnonlinearneuralnetwork,codingofinformation.I.INTRODUCTIONConstructionandimplementationofmathematicalmodelsthatyieldahighdegreeofprotectionofinformationareamongpresentchallengesofcryptography.Modelsthatfeaturesignificantchangesofthestructureoftheincominginformationalsignalareofspecialinterest.Inthispaper,westudytransformationsofanincomingsignalbyasingleoscillatoryneuronaswellasbyasystemofnonlinearoscillatoryneuronscoupledbysynapticweightcoefficients.Thesecoefficientsarechosentoendowtheartificialnonlinearneuralnetworkwiththetopologyofachainoraring.Theinteractionbetweentheneuronsisassumedtobeof“dipole–dipole”type.Weshowthattheproposedmodelschangethestructure(shape,amplitude,frequencyandphase)ofanincominginformationalsignalinasignificantway.Thestructureofthearticleconsistsof5sections:Thefirstsection(introduction)indicatestheneedtobuildandimplementmathematicalmodelsbasedonneuralnetworkswithnonlinearoscillatoryneuronsforcryptographicsystems.Thesecondsectionpresentsananalysisofscientificpapersrelatedtothetransformationofthestructureofinputsignalsbyasingleneuronorneuralnetwork.Thethirdsectiondescribesthepurposeandmethodofstudyingtheprocessesofmorphologytransformationoftheinputsignalusingachainorringnetworkofnonlinearoscillatoryneurons.Inthefourthsection,amathematicalmodelofthechainandringnetworkofnonlinearoscillatoryneuronsisconstructed.Thefifthsectionpresentsthesolutionofthemathematicalmodelofthechainandringnetwork2StructuralTransformationsofIncomingSignalbyaSingleNonlinearOscillatoryNeuronorbyanArtificialNonlinearNeuralNetworkCopyright©2019MECSI.J.IntelligentSystemsandApplications,2019,8,1-10ofnonlinearoscillatoryneuronsandacomputerexperimenttotransformthemorphologyoftheinputsignalsbyasingleneuronandasystemofneurons.Theresultsofstudiesofthecriteriafortheoccurrenceofresonanceeffectsinanonlinearoscillatoryneuronarealsopresented.Itisshownthatresonanceeffectsinanonlinearoscillatoryneuronoccurundertheconditionthatthefrequencyoftheexternalnon-stationarysignalcoincideswiththeintrinsicdynamicsoftheneuron.Thecodingofinformationonthebasisoffrequencymodulationusinganonlinearoscillatoryneuronisproposed.Decodingusingtheinverseoperator,whichactsonthevectoroftheoutputsignal,isproposed.II.RELATEDWORKSAttheinitialstagesofprocessingofsensorydata,waveletanalysisisaneffectiveinstrumentinthedeterminationoftheinformativecomponentintheneuralsignalsthatarebeingregistered.Usuallythisdeterminationisperformedbyanalysisofthestructureofthepoint-wiseprocesses,thatis,analysisofthetime-frequencydynamicsofneuralresponses[1–8],inwhichtheinformationiscarriedbythetimesatwhichimpulses(spikes)aregeneratedratherthantheshapeoftheseresponses[9].Themechanismsbywhichthespikesaregeneratedareonlypartiallyunderstood[10],whilethewaysinwhichnonlinearoscillatoryneuronstransformthestructureofanincominginformationsignalhavenotbeeninvestigated,tothebestofourknowledge.In[2–5,8]thetransformationofsignalsbyasensoryneuron(thresholddevice)isanalyzed;theanalysisdoesnottakeintoaccountthedynamicsoftheneuronitself.Ithasbeenshown,bymeansofclassicalmodelsofthresholdsystemssuchas“integrate-and-fire”[2–4]and“thresholdcrossing”[5,8],thatdi