关于脉冲摄动微分系统稳定性的研究

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1、-20112011---........................................................................1........................................................................3.........................51.1...............................................................51.2...

2、.......................................................61.3..................71.4Lyapunov.............141.5T-...........20........................272.1..............................................................272.2.......................................

3、..................272.3................................292.4.......34.......................................................................45..................................................................48...............................................

4、.............................49---(250014)[13−20].[9−11],[11].x′(t)=f(t,x),t=tk,∆x=Ik(x),t=tk,x(t+0)=x0,k=1,2,3···,f(t,x)=F(t,x)+R(t,x),Ik(x)=I∗k(x)+Qk(x),R,Qx′(t)=f(t,x),t=τk(x),∆x=Ik(x),t=τk(x),(I)′(I)---x(t+0)=x0,k=1,2,3···,f(t,x)=F

5、(t,x)+R(t,x),R,IkT-DiniT-T-1---Lyapunov(h0,h)−T-O175.212---StabilityAnalysisofImpulsivePerturbedDifferential SystemsFengliYuSchoolofMathematicalSciences,ShandongNormalUniversityJinan,Shandong,250014,P.R.ChinaABSTRACTPerturbeddifferentialsystemsareappliedwidel

6、yinthefieldofnaturalscience.Itisaimportantpartoftheresearchaboutdifferentialsystems.Thatisbecauseinreallife,whenweestablishamathematicalmodelbydifferentialsystemsforthespecificissue,therearealwayssometinyperturbedforcethatcannotbespecificallyidentified,andthesepe

7、rturbedforceoftenhaveinfluencetothesystem.Theseperturbedforceiscalledperturbation,andthecorrespondingdifferentialsystemsknownastheperturbeddifferen-tialsystems.Inrecentyears,forthetheoreticalsignificanceandthevalueofapplicationoftheperturbeddifferentialsystems,t

8、hestudyofwhichhasmadesomeprogress[13−20].Atthesametime,impulseasainstantaneouschangephenomenon,whichisverycommoninthenature.Asthedevelopmentofscienceresearch,thedifferentialsystemswithim-pulsesandpertur