復(fù)雜網(wǎng)絡(luò)的若干動力學(xué)問題研究.pdf

1、東南大學(xué)碩士學(xué)位論文復(fù)雜網(wǎng)絡(luò)的若干動力學(xué)問題研究姓名：黃淦申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：曹進(jìn)德20080102AbstractInrecentyears，investigationsinboththeoryandapplicationofcomplexnetworkshavereceivedconsiderableattention，andmanydynamicsproblemsincomplexnetworkshavebe

2、comeinterestingresearchtopicsInthispaper，wefocusontheproblemsofopinionformationbyintroducingasimplemodelwithacertaincommunitystructure，themultistabilityandthestateestimationproblemoftheneuralnetworksThemainresultsarea8fo

3、llows：Firstlyutilizingcomputersimulationandthemethodofstatistics，westudiedtheopimonformationprobleminasimplemodelBothsimulationandanalysisweredoneintheabsenceandpresenceofnoiseItcouldbefoundthatthestrengthofthecommunitym

4、ainlycomesfromitscohesioninsidethecommunityWhileitisalsoinfluencedbythepopulationofthecommunityandthenoisecanalsobringsomeinterestingandunexpectedresultsSecondlybyapplyingLinearMatrixInequality(LMI)approachandsomeotherme

5、thod，weinvestigatedthemultistabilityissuesoftheneuralnetworkindifferentways：a1BoththedelaydependentanddelayindependentresultswerederivedComparedwiththeexistingresults，itislessconservativeFurthermore，asimpleexamplewasgive

6、ntoshowthecomplexityofthedelaydependentmultistabilityintheneuralnetworksb1Duetothelimitontheselfconnectionweightsoftheneuralnetworksintheexistingmultistabilityreuslts，weconsideredthemultistabilityissuesofBAMneuralnetwork

7、s，andderivedsomemultistabilityresultsc、AkindofneuralnetworkwithpiecewisediscontinuousactivationfunctionWasproposedandthecorrespondingmultistabilityresultswerederivedAlsowediscussedtheupperlimitofthenumberofthestableequil

8、ibriaintheneuralnetworksFinallytherobuststateestimationissueWasstudiedforuncertainneuralnetworkForgivenstateestimatorgainmatrix，theerrorboundWnsderivedByusingstabilitytheoryandLMIapproach，thedesignoftherobuststateestimat