资源描述：
《Tan_et_al-2016-Mathematical_Methods_in_the_Applied_Sciences》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。
1、ResearchArticleReceived17March2015PublishedonlineinWileyOnlineLibrary(wileyonlinelibrary.com)DOI:10.1002/mma.3732MOSsubjectclassification:34A36;34C27Existenceandglobalexponentialstabilityofalmostperiodicsolutionfordelayedcompetitiveneuralnetworkswithdiscontinuousactivationsab*†YanxiangT
2、anandKeJingCommunicatedbyG.SvetlinInthispaper,westudyaclassofdelayedcompetitiveneuralnetworkswithdiscontinuousactivations.WithoutassumingtheboundednessandlocalLipschizianontheactivationfunctions,somenewcriteriaensuringtheexistenceandglobalexponentialstabilityofalmostperiodicsolutionsfo
3、rtheneuralnetworkmodelconsideredinthisworkareestablishedbyconstructingsomesuitableLyapunovfunctionalsandemployingthetheoryofnonsmoothanalysis.Finally,wepresentsomeapplicationsandnumericalexampleswithsimulationstoshowtheeffectivenessofourmainresults.Copyright©2016JohnWiley&Sons,Ltd.Keyw
4、ords:delaycompetitiveneuralnetworks;discontinuousactivation;almostperiodicsolution;globalexponentialstability1.IntroductionInrecentyears,variousneuralnetworkssuchascellularneuralnetworks,Hopfieldneuralnetworks,bidirectionalassociativememoryneuralnetworks,andCohen–Grossbergneuralnetworks
5、withdiscontinuousright-handsideshavebeenextensivelyinvestigatedinboththeoryandapplication,andtheyhavebeensuccessfullyappliedtosignalprocessing,patternrecognition,associativememory,andoptimizationproblems(see[1–14]andthereferencestherein).Manyresultsofthesein-depthresearchmainlyfocusedo
6、nthedynamicsoftheequilibriumpointorperiodicsolution.Aspointedoutin[15],thevariationoftheenvironmentplaysanimportantroleinreal-word,periodicallyvaryingenvironment,andalmostperiodicallyvaryingenvironmentsarefoundationsforthetheoryofdynamicalsystem.Comparedwithperiodiceffects,almostperiod
7、iceffectsaremorefrequent.Therefore,theeffectsofthealmostperiodicenvironmentontheevolutionarytheoryhavebeentheobjectofintensiveanalysisbynumerousauthors,andsomeoftheseresultscanbefoundin[16–21]andthereferencestherein.Recently,Meyer-BaRseetal.proposedtheso-calledcompetitiveneuralnetwor
