隨機(jī)Cohen-Grossberg神經(jīng)網(wǎng)絡(luò)模型的若干問題研究.pdf

1、長(zhǎng)沙理工大學(xué)碩士學(xué)位論文隨機(jī)CohenGrossberg神經(jīng)網(wǎng)絡(luò)模型的若干問題研究姓名：陳萍申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：概率論與數(shù)理統(tǒng)計(jì)指導(dǎo)教師：黃創(chuàng)霞20100401ABSTRACTInrecentyears，thedynamicalissuesofstochasticdelayedneuralnetworkshavea上tractedworldwideattentionManyinterestingstabilitycriteriafo

2、rtheequilibriumsolutionsofstochasticdelayedneuralnetworkshavebeenobtainedInthisthesis，weinvestigatethepthmomentexponentialstabilityandthealmostsureexponentialstabilityoftheequilibriumsolutionsforstochasticCohen—Grossberg

3、neurMnetworks(CGNN)withtimevaryingdelaysandunboundeddistributeddelaysThethesisCOIlsistsoffourchaptersAstheintroduction，inChapterOne，thebackgroundanddevelopmentofthestudyofthestabilityforstochasticneuralnetworksarepresent

4、edThemotivationsandoutlineofthisworkarealsogiveninthischapterInChapterTwo，somefundamentalknowledge，includingthebasicconceptsofstochasticdifferentialequation，stochasticprocesses，Brownmotions，It5integralandIt5formula，isbri

5、eflyintroducedInChapterThree，thestabilityoftheequilibriumsolutionsforstochasticCGNNwithtime—varyingdelaysarestudiedWiththehelpofthesemimartingMeconvergeneetheorem，somesufficientcriteriaareestablishedforthealmostsureexpon

6、entialstabilityofthesystemUsingTt5formula，theDini—derivativeandthetechniqueofsomeinequalities，weobtainsomesufficientcriteriatocheckthepthmomentexponentialstabilityforageneralstochasticCGNNwithtimevaryingdelays：then，apply

7、ingBurkholder。DavidsGundyinequalityandBorelCantell’slemmaafamilyofsufficientconditionsisgivenforcheckingthealmostsureexponentialstabilityofthismodelFinally，inChapterFour，thestabilityoftheequilibriumsolutionsforstochastic

8、CGNNwithunboundeddistributeddelaysareinvestigatedWithoutassumingthesmoothness，byconstructingsuitableLyapunovfunction，employingthescmimartin’galeconvergencetheoremandthetechniqueofsomeinequalities，weobtainsomesufficientcr

9、iteriatocheckthealmostexponentialstabilityofthemodelAnexampleisalsogiventoillustratethee雎ctivenessoftheobtainedresultsKeyWords：stochasticCohen—Grossbergneuralnetworks；It8formula；Lyapunovfunction；pthmomentexponentialstabi