DISSIPATIVITY AND EXPONENTIAL STABILITY OF θ-METHODS FOR SINGULARLY PERTURBED DELAY DIFFERENTIAL EQUATIONS WITH A BOUNDED LAG

(整期优先)网络出版时间:2003-06-16
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Thispaperdealswithanalyticandnumericaldissipativityandexponentialstabilityofsingularlyperturbeddelaydifferentialequationswithanyboundedstate-independentlag.Sufficientconditionswillbepresentedtoensurethatanysolutionofthesingularlyperturbeddelaydifferentialequations(DDEs)withaboundedlagisdissipativeandexponentiallystableuniformlyforsufficientlysmallε>0.Wewillstudythenumericalsolutiondefinedbythelinearθ-methodandone-legmethodandshowthattheyaredissipativeandexponentiallystableuniformlyforsufficientlysmallε>0ifandonlyifθ=1.